Prof. Zhou-Ping XIN

Last updated: Feb 2, 2024

Prof. Zhou-Ping XIN
(辛周平教授)

Executive Director & William M. W. Mong Professor of Mathematics


EDUCATION

Ph.D. in Mathematics, University of Michigan, Ann Arbor, 1985-1988

B.S. and M.S. in Mathematics, Northwestern University, 1978-1984

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MAIN RESEARCH INTERESTS

Partial differential equations

Fluid dynamics

Mathematical Physics

Nonlinear waves

Numerical analysis

Applied mathematics

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PROFESSIONAL EXPERIENCE

Executive Director, The Institute of Mathematical Sciences, The Chinese University of Hong Kong, since 05/2020

William M. W. Mong Professor of Mathematics, The Institute of Mathematical Sciences & Department of Mathematics, The Chinese University of Hong Kong, since 08/2004

Professor of Mathematics, The Institute of Mathematical Sciences & Department of Mathematics, The Chinese University of Hong Kong, 04/2000 - 07/2004

Associate Director, The Institute of Mathematical Sciences The Chinese University of Hong Kong, 08/1998-04/2020

Professor of Mathematics, Courant Institute, USA, 09/1996 - 09/2001

Associate Professor, Courant Institute, USA, 09/1993 - 08/1996

Member, Institute for Advanced Studies, Princeton, USA, 09/1993 - 08/1994

Assistant Professor, Courant Institute, USA, 09/1990 - 08/1993

Courant Instructor, Courant Institute, USA, 09/1988 - 08/1990

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PROFESSIONAL SOCIETIES

Member, and Member of Academic Committee, International Consortium of Chinese Mathematicians (ICCM) since 08/2016

Council Member at Large, Hong Kong Mathematical Society, since 05/2016

President, Hong Kong Mathematical Society, 05/2012 - 04/2016

Vice President, Hong Kong Mathematical Society, 05/2004 - 04/2012

Member, Hong Kong Mathematical Society, since 09/1998

Member, American Mathematical Society, 09/1985 - 08/2001

Society for Industrial and Applied Mathematics, 09/1985 - 08/2001

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AWARDS AND HONORS

Top 1000 Scientists in Mathematicians, 2022

Qin Yuan Xun Mathematical Award, 08/2019

Distinguished Paper Award (Silver), International Consortium of Chinese Mathematicians, 2017

Changjiang Scholar, Ministry of Education of China, 2006-2008

Morningside Gold Medalist in Mathematics, International Congress of Chinese Mathematicians, 12/2004

Invited Address, International Congress of Mathematicians, 08/2002

Sloan Research Fellowship Award, 1991-1993, USA, 04/1991

Presidential Fellow, NYU, USA, 09/1993

Best Thesis Award in Mathematics 1988, University of Michigan, Ann Arbor, USA, 04/1989

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EXTERNAL SERVICE (outside CUHK)

Member, Scientific Committee, Tsinghua Sanya International Mathematics Forum, since 2023

Member, Scientific Committee, Hong Kong Society for Industrial and Applied Mathematics, Hong Kong, 2022-2023

Vice Chair, Scientific Committee, Center of Applied Mathematical at Greater Bay Area, China, since 2020

Member, Scientific Committee, National Tianyuan Center of Mathematics, Central, China, since 2019

Member, Physical Science Panel of RGC, HKRGC, since 2018

Member, Scientific Committee, 教育部科學工程實驗室, Shanghai Jiao Tong University, since 2018

Member, Scientific Committee, National Tianyuan Center of Mathematics, Northwest, China, since 2018

Member, Committee for Hong Kong PhD Fellowship Scheme, HKRGC, 16/2017-17/2018

Member, Academic Steering Committee, Tianyuan Foundation, NSFC, since 2016

Member, Review Committee, Institute of Mathematics, CAS, 2016

Member, Scientific Committee, National Tianyuan Center of Mathematics, Southeast, China, since 2015

Member, Scientific Committee, CMSA, Harvard University, USA, since 2014

Member, Scientific Committee, YMSC, Tsinghua University, China, since 2010

Chair, Scientific Committee, Annual National Summer School on PDEs, since 2003

Member, Scientific Committee, International Congress on Hyperbolic Problem, 2001-2010

Member, Scientific Committee, Morningside Center, CAS, China, since 1998

Member, Scientific Committee, International Congress for Chinese Mathematicians, since 1998

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VISITING AND GUEST PROFESSORSHIP

Visiting Associate Professor, CMSA, Harvard University, 10/2015 - 11/2015

Visiting Professor, Huanan Normal University, China, since 09/2017

Special Invited Professor, Northwestern University, since 09/2003

Special Invited Professor, Capital Normal University, since 05/2002

Visiting Professor of Mathematics, CUHK, Hong Kong, 09/1998 - 03/2000

Distinguished visitor, University of California, USA, 09/1999 - 10/1999

Co-Current Prof. of Math., Fudan University, 05/2000 - 05/2003

Co-Current Prof. of Math., Zhongshan University, 07/1999 - 07/2002

Member, Mittag-Leffler Institute, Sweden, 09/1997 - 10/1997

Visiting Associate Professor, Harvard University, USA, 08/1995 - 08/1996

Invited Professor, University of Paris 7, Paris, 05/1996 - 07/1996

Invited Professor, ETH, Zurich, 01/1996 - 02/1996

Invited Professor, Ecole Normale Superieuse, Paris, 05/1995 - 07/1995

Invited Professor, Inst. le Applicazioni del Calcolo, Roma, 04/1994 - 05/1994

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POSTGRADUATE STUDENTS TRAINING

Graduated PhD students (Total: 41; 38 of which were from CUHK)

Graduated MPhil students (Total: 31; 28 of which were from CUHK)


Current PhD Students (Total: 11)

Current MPhil Students (Total: 2)

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EDITORSHIP

Co-Editor-In-Chief, Methods and Applications of Analysis, since 1998

Main Associate Editor, Journal of Mathematical Physics, since 2017

Main Associate Editor, Mathematical Methods in Applied Sciences, since 2014


Editorial Board Members/Associate Editors:

SIAM Journal of Mathematical Analysis, 1996-2004

Journal of Mathematics of Kyoto University, since 2006

Asian Journal of Mathematics, since 1998

Mathematical Models & Methods in Applied Sciences, since 2008

Communications in Mathematical Sciences, since 2004

Science in China, Series A, since 1998

Acta Mathematica Sinica (English Series), since 1996

Acta Mathematica Applica Sinica (English Series), since 1996

Kinetic and Related Models, since 2006

Journal of Applied Analysis and Computation, since 2002

Journal of Hyperbolic Partial Differential Equations, 1996-2004

Journal of Partial Differential Equations, since 2000

Annals of Applied Mathematics, since 2012

Pure and Applied Mathematics Quarterly, since 2016

Applied Mathematics Journal of Chinese Universities, Series A, since 2002

Advanced Lectures in Mathematics, since 2002

SCIENCE CHINA Mathematics, 2023-2027

Communications in Mathematical Research, since 2019

Chinese Annals of Mathematics, Series B, since 2021

Journal of Hyperbolic Differential Equation, since 2022

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RESEARCH GRANTS

PI, RGC General Research fund 2023/24, On Entropy-Bounded Solutions to the Compressible Navier-Stokes Equations in the Presence of Vacuum, 14301023, 01/01/2024 – 31/12/2026

PI, RGC General Research Fund 2021/22, Well-Posedness of The Contact Discontinuities for the Ideal MHD, 14301421, 01/01/2022 – 31/12/2024

PI, RGC General Research Fund 2019/20, Regularity estimates of Hessian and Curvature equations, 14300819, 01/11/2019 – 31/10/2023

PI, RGC General Research Fund 2019/20, Vacuum Dynamics for the Full Compressible Navier-Stokes Equations, 14302819, 01/01/2020 - 30/06/2023

PI, RGC General Research Fund 2017/18, On Some Problems for Steady Compressible Euler Systems, 14300917, 01/01/2018 - 31/12/2021

PI, RGC General Research Fund 2017/18, Weak and Strong Solutions to the Primitive Equations with Full or Horizontal Viscosity but No Diffusivity, 14302917, 01/09/2017 - 28/02/2021

PI, RGC General Research Fund 2015/16, On Periodic Solutions to the One-Dimensional Compressible Euler Equations, 14305315, 01/01/2016 - 30/06/2019

PI, NSFC/RGC Joint Research Scheme, On Mathematical Theory of the Compressible Fluid-dynamical Equations, N-CUHK443/14, 01/01/2015 - 31/12/2018

PI, RGC General Research Fund 2013/14, On Steady Compressible Transonic Flows, 404813, 01/10/2013 - 30/09/2017

PI, Focused Innovations Scheme (Scheme B), Applied Analysis and Scientific Computations, 01/02/2013 - 30/06/2017

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LIST OF RESEARCH OUTPUTS OR CREATIVE WORKS

Publications (Total: 190) (Citations: 12451, as at March 2022; Source: Google Scholar)

Refereed Journal Papers (total: 173):

  1. A conservative hybrid deep learning method for Maxwell–Ampère–Nernst–Planck equations, (with Cheng Chang, Tieyong Zeng), Journal of Computational Physics, 501, https://doi.org/10.1016/j.jcp.2024.112791 (2024).

  2. Existence of Multi-Dimensional Contact Discontinuities for the Ideal Compressible Magnetohydrodynamics, (with Yanjin Wang), Communications on Pure and Applied Mathematics, http://doi.org/10.1002/cpa.22148 (2023).

  3. On Regular Solutions for Three-Dimensional Full Compressible Navier-Stokes Equations with Degenerate Viscosities and Far Field Vacuum, (with Qin Duan, Shengguo Zhu), Archive for Rational Mechanics and Analysis, 247, No. 1, Paper No. 3, 71 pp. (2023).

  4. Incompressible Impinging Jet Flow With Gravity, (with Jianfeng Cheng, Lili DU), Calculus of Variations and Partial Differential Equations, 62:110, DOI: 10.1007/s00526-023-02448-z (2023).

  5. Local and global well-posedness of entropy-bounded solutions to the compressible Navier-Stokes equations in multi-dimensions (with Jinkai Li), Sci China Math, 65, https://doi.org/10.1007/s11425-022-2047-0 (2022).

  6. Entropy-Bounded Solutions to the One-Dimensional Heat Conductive Compressible Navier-Stokes Equations with Far Field Vacuum, (with J. K. Li), Communications on Pure and Applied Mathematics, Vol. 75, No. 11, 2393-2445 (2022).

  7. On the vanishing dissipation limit for the incompressible MHD equations on bounded domains, (with Qin Duan, Yuelong Xiao), Sci. China Math., Vol. 65, No. 1, 31-50 (2022).

  8. Global Well-Posedness of the Inviscid Heat-Conductive Resistive Compressible MHD in a Strip Domain, (with Yanjin Wang), Commun. Math. Res., Vol. 38, No. 1, 1-27 (2022).

  9. Subsonic flows past a profile with a vortex line at the trailing edge, (with Jun Chen, Aibin Zang), SIAM J. Math. Anal., 54, No. 1, 912-939 (2022).

  10. Asymptotic stability of shock profiles and rarefaction waves under periodic perturbations for 1-D convex scalar viscous conservation laws, (with Qian Yuan, Yuan Yuan), Indiana Univ. Math. J., Vol. 70, No. 6, 2295-2349 (2021).

  11. Steady Compressible Radially Symmetric Flows with Nonzero Angular Velocity in an Annulus, (with S. K. Weng, H. W. Yuan), JDE, 286, 433-454 (2021).

  12. On Some Smooth Symmetric Transonic Flows with Nonzero Angular Velocity and Vorticity, (with S. K. Weng, H. W. Yuan), submitted to M3AS: Math. Models Methods Appl. Sci., 31, no. 13, 2773-2817 (2021).

  13. Global well-posedness of regular solutions to the three-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosities and vacuum, (with S. G. Zhu), Advances in Mathematics, 393, https://doi.org/10.1016/j.aim.2021.108072 (2021).

  14. Global Well-Posedness of Free Interface Problems for the Incompressible Inviscid Resistive MHD, (with Yanjin Wang), Commun. Math. Phys, 388, No. 3, 1323-1401 (2021).

  15. Regular subsonic-sonic flows in general nozzles, Advances in Mathematics, (with C. P. Wang), Vol. 380, https://doi.org/10.1016/j.aim.2021.107578 (2021).

  16. Well-posedness of three-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosities and far field vacuum, (with S. G. Zhu), J. Math. Pures Appl. (9) 152, 94-144 (2021).

  17. Vanishing Viscosity and Surface Tension Limits of Incompressible Viscous Surface Waves, (with Y. J. Wang), SIAM J. Math. Anal., 53, No. 1, 574-648 (2021).

  18. On Admissible Locations of Transonic Shock Fronts for Steady Euler Flows in an Almost Flat Finite Nozzle with Prescribed Receiver Pressure, (with B. X. Fang), CPAM, Vol. 74, Iss. 7, 1493-1544 (2021).

  19. Optimal Decay for the Compressible Navier-Stokes Equations without Additional Smallness Assumptions, (with Jiang Xu), JDE, 274, 543-575, (2021).

  20. Asymptotic Stability of Shock Waves and Rarefaction Waves under Periodic Perturbations for 1-D Convex Scalar Viscous Conservation Laws, (with Qian Yuan, Yuan Yuan), SIAM, 51, No. 4, 2971-2994 (2020).

  21. Structural stability of the transonic shock problem in a divergent three dimensional axisymmetric perturbed nozzle, (with Shangkun Weng, Chunjing Xie), SIAM J. Math. Anal., 53, No. 1, 279-308 (2020).

  22. Entropy bounded solutions to the one-dimensional compressible Navier-Stokes equations with zero heat conduction and far field vacuum, (with J. K. Li), Advances in Math., 361 (2020).

  23. Axisymmetric 3D Euler-αEquations without Swirl: Existence, Uniqueness, and Radon Measure Valued Solutions, (with Quansen Jiu, Dongjuan Niu, Edriss S. Titi), Pure and Applied Functional Analysis, Vol. 4, No. 3, 573-588 (2019).

  24. On an elliptic free boundary problem and subsonic jet flows for a given surrounding pressure, (with Chunpeng Wang), SIAM J. Math. Anal., Vol. 51, no. 2, 1014-1045 (2019).

  25. Asymptotic Stability of Shock Waves and Rarefaction Waves Under Periodic Perturbations for 1-D Convex Scalar Conservation Laws, (with Qian Yuan, Yuan Yuan), SIMA, Vol. 51, Iss. 4, DOI:10.1137/18M1192883 (2019).

  26. Global Well-Posedness and Large Time Asymptotic Behavior of Classical Solutions to the Compressible Navier-Stokes Equations with Vacuum, (with Jing Li), Annals of PDE, Vol. 5, No. 1, Art. 7, pp.37 (2019).

  27. Non-Existence of Classical Solutions with Finite Energy to the Cauchy Problem of the Compressible Navier-Stokes Equations, (with H. L. Li, Y. X. Wang), ARMA, Vol. 232, Issue 2, 557-590, 2019.

  28. Smooth Transonic Flows of Meyer Type in De Laval Nozzles, (with C. P. Wang), Archive for Rational Mechanics and Analysis, Vol. 232, No. 3, 1597 - 1647, 2019.

  29. On scaling invariance and type-I singularities for the compressible Navier-Stokes equations, (with Z. Lei), Science China Mathematics, DOI 10.1007/s11425-018-9363-1 (2019).

  30. Global classical solutions to two-dimensional compressible Navier-Stokes equations with large data in R², (with Q. Jiu, Y. Wang), Physica D: Nonlinear Phenomena, Vol. 376-377, 180-194, 2018.

  31. Stability analysis for the incompressible Navier-Stokes equations with Navier boundary conditions, (with S. J. Ding, Q. R. Li), J. Math. Fluid Mech., Vol. 20, no. 2, 603-629, 2018.

  32. Uniform regularity for the free surface compressible Navier-Stokes equations with or without surface tension, (with Y. Mei, Y. Wang), Math. Models Methods Appl. Sci., 28, no. 2, 259-336, 2018.

  33. A deformation-curl decomposition for three dimensional steady Euler equations, (with Shangkun Weng), Scientia Sinica Mathematica 49 (2), 307 (2018).

  34. Boundary layer problems in the vanishing viscosity-diffusion limits for the incompressible MHD system (in Chinese), (with S. Wang), Sci Sin Math, Vol. 47, No. 10, 1303-1 326, doi: 10.1360/N012016-00211, 2017.

  35. Global entropy solutions to weakly nonlinear gas dynamics, (with P. Qu), Adv. Math. 316, 292-355, 2017.

  36. On sonic curves of smooth subsonic-sonic and transonic flows, (with C. P. Wang), SIAM J. Math. Anal., Vol. 48, no. 4, 2414-2453, 2016.

  37. Global existence of weak solutions to the non-isothermal nematic liquid crystals in 2D, (with J. K. Li), Acta Math. Sci. Ser. B (Eng), Vol. 36, no. 4, 973-1014, 2016.

  38. Two dimensional subsonic Euler flows past a wall or a symmetric body, (with C. Chen, L. L. Du, C. J. Xie), Arch. Ration. Mech. Anal., Vol. 221, no. 2, 559-602, 2016.

  39. Nonlinear Asymptotic Stability of the Lane-Emden Solutions for the Viscous Gaseous Star Problem with Degenerate Density Dependent Viscosities, (with T. Luo, H. H. Zeng), Commun. Math. Phys, 347(3), 657-702, 2016.

  40. On formation of singularity for non-isentropic Navier-Stokes equations without heat-conductivity, (with X. D. Huang), Discrete Conti. Dyn. Syst., 36, No. 8, 4477-4493, 2016.

  41. On the uniqueness of weak solutions to the Ericksen-Leslie liquid crystal model in R², (with J.K. Li, E. Titi), Math. Models Methods Appl. Sci. 26, no. 4, 803-822, 2016.

  42. Non-uniqueness of admissible weak solutions to compressible Euler systems with source terms, (with T.W. Luo, C.J. Xie), Adv. Math. 291, 542-583, 2016.

  43. On nonlinear asymptotic stability of the Lane-Emden solutions for the viscous gaseous star problem, (with T. Luo, H.H. Zeng), Adv. Math. 291, 90-182, 2016.

  44. Remarks on blow-up of smooth solutions to the compressible fluid with constant and degenerate viscosities, (with Q.S. Jiu, Y.X Wang), J. Differential Equations 259, no. 7, 2981-3003, 2015.

  45. Long time existence of entropy solutions to the one-dimensional non-isentropic Euler equations with periodic initial data, (with P. Qu), ARMA, Vol. 216, No. 1, (2015), 221-259.
  46. Global smooth supersonic flows in infinite expending nozzles, (with C. P. Wang), SIAM J. Math. Anal. 47, no. 4, 3151-3211, 2015.

  47. Uniform regularity and vanishing viscosity limit for the compressible Navier-Stokes with general Navier-slip boundary conditions in 3-dimensional domains, (with Y. Wang, Y. Yong), SIAM J. Math. Anal. 47, no. 6, 4123-4191, 2015.

  48. Blow-up criteria of strong solutions to the Ericksen-Leslie system in R³, (with M. C. Hong, J. K. Li), Comm. Partial Diff. Eqns., 39 (2014), No. 7, 1284-1328.

  49. Low Mach number limit for the full compressible magnetohydrodynamic equations with general initial data, (with S. Jiang, Q. C. Ju, F. C. Li), Adv. Math., 259 (2014), 384-420.

  50. Steady subsonic ideal flows through an infinitely long nozzle with large vorticity, (with L. L. Du, C. J. Xie), Comm. Math. Phys., 328 (2014), No. 1, 327-354.
  51. Subsonic irrotational flows in a finitely long nozzle with variable end pressure, (with L. L. Du, S. K. Weng), Comm. Partial Diff. Eqns., 39 (2014), No. 4, 666-695.

  52. Global Well-Posedness of 2D Compressible Navier-Stokes Equations with Large Data and Vacuum, (with Q. Jiu, Y. Wang), J. Math. Fluid Mech., 16 (2014), No. 3, 483-521.

  53. Well-Posedness for the Motion of Physical Vacuum of the Three-dimensional Compressible Euler Equations with or without Self-Gravitation, (with T. Luo, H. H. Zeng), ARMA, Vol. 213, Iss. 3 (2014), 763-831.

  54. Global in time stability of steady shocks in nozzles, (with J. Rauch, C.J. Xie), Séminaire Laurent Schwartz-Équations aux dérivées partielles et applications, Année 2011-2012, Exp. No. II, 11 pp., Sémin. Équ. Dériv. Partielles, École Polytech., Palaiseau, 2013.
  55. On 3D Lagrangian Navier-Stokes α model with a class of vorticity-slip boundary conditions, (with Y. Xiao), J. Math. Fluid Mech., 15 (2013), no. 2, 215-247.

  56. Global stability of steady transonic Euler shocks in quasi-one-dimensional nozzles, (with J. Rauch, C. J. Xie), J. Math. Pures Appl. (9) 99 (2013), no. 4, 395-408.

  57. Existence of Weak Solutions for a Two-dimensional Fluid-rigid Body System, (with Y. Wang), J. Math. Fluid Mech., Vol. 15, Iss. 3 (2013), 553-566.

  58. On Blowup of Classical Solutions to the Compressible Navier-Stokes Equations, (with W. Yan), Comm. Math. Phys. 321, Iss. 2 (2013), 529-541.

  59. On a Degenerate Free Boundary Problem and Continuous Subsonic-Sonic Flows in a Convergent Nozzle, (with C. P. Wang), ARMA, Vol. 208, Iss. 3 (2013), 911-975.

  60. Transonic Shocks for the Full Compressible Euler System in a General Two-Dimensional De Laval Nozzle, (with J. Li, H. Yin), ARMA, Vol. 207, Iss. 2 (2013), 533-581.

  61. Vacuum behaviors around rarefaction waves to 1D compressible Navier-Stokes equations with density-dependent viscosity, (with Q. Jiu, Y. Wang), SIAM J. Math. Anal., Vol. 45, No. 5 (2013), 3194-3228.

  62. Global well-posedness of the Cauchy problem of two-dimensional compressible Navier-Stokes equations in weighted spaces, (with Q. S. Jiu, Y. Wang), JDE, Vol. 255, No. 3, 351-404, 2013.

  63. On the Inviscid Limit of the 3D Navier-Stokes Equations with Generalized Navier-Slip Boundary Conditions, (with Y. L. Xiao), Comm. Math. Stat., Vol. 1, Iss. 3 (2013), 259-279.

  64. A new boundary condition for the three-dimensional Navier-Stokes equation and the vanishing viscosity limit, (with Y. L. Xiao), J. Math. Phys. 53 (2012), no. 11, 115617, 15 pp.

  65. The Boltzmann equation with soft potentials near a local Maxwellian, (with T. Yang, and H. Yu), ARMA, Vol. 206, Iss. 1 (2012), 239-296.

  66. Global existence of solutions of the liquid crystal flow for the Oseen-Frank model in R², (with M. C. Hong), Adv. Math., 231 (2012), 1364-1400.

  67. Transonic Shock Solutions for a System of Euler-Poisson Equations, (with T. Luo), CMS, Vol. 10, No. 2, 419-462 (2012).

  68. Lagrange structure and dynamics for solutions to the spherically symmetric compressible Navier-Stokes equations, (with Z. H. Guo, H. L. Li), Comm. Math. Phys. 309 (2012), no. 2, 371-412.

  69. Analytical Solutions to the Compressible Navier-Stokes Equations with Density-dependent Viscosity Coefficients and Free Boundaries, (with Z. Guo), JDE 253, 1-19 (2012).

  70. Global Well-Posedness of Classical Solutions with Large Oscillations and Vacuum to the Three-Dimensional Isentropic Compressible Navier-Stokes Equations, (with X. D. Huang, J. Li), CPAM, 65 (2012), 549-585.

  71. Vanishing Viscous Limits for 3D Navier-Stokes Equations with a Navier-Slip Boundary Condition, (with L. Z. Wang, A. B. Zang), Journal of Mathematical Fluid Mechanics, 14 (2012), No. 4, 791-825.

  72. Stability of Transonic Shock Solutions for One-Dimensional Euler-Poisson Equations, (with T. Luo, J. Rauch & C. J. Xie), Arch. Rat. Mech. Anal. (2011), 202, No. 3, 787-827.

  73. Serrin-Type Criterion for the Three-Dimensional Viscous Compressible Flows, (with J. Li, X. Huang), SIAM J. Math. Anal. 43, 1872-1886 (2011).

  74. Analyticity of the semigroup associated with the fluid-rigid body problem and local existence of strong solutions, (with Y. Wang), J. of Func. Anal. (2011), 261, No. 9, 2587-2616.

  75. Subsonic Flows in a Multi-Dimensional Nozzle, (with L. L. Du & W. Yan), Arch. Rat. Mech. Anal., Vol. 201, No. 3, 965-1012 (2011).

  76. Remarks On Vanishing Viscosity Limits for the 3D Navier-Stokes Equations with a Slip Boundary Condition, (with Y. L. Xiao), Chin. Ann. Math., 32B(3), 2011, 321-332 (2011).

  77. Optimal Hölder continuity for a class of degenerate elliptic problems with an application to subsonic-sonic flows, (with C. P. Wang), Comm. PDE 36, No. 5, 873-924 (2011).

  78. Stability of Rarefaction Waves to the 1D Compressible Navier-Stokes Equations with Density-Dependent Viscosity, (with Q. Jiu, Y. Wang), Comm. PDEs, Vol. 36, No. 4, 602-634 (2011).

  79. Blowup Criterion for Viscous Baratropic Flows with Vacuum States, (with X. Huang, J. Li), Comm. Math. Phys., 301, 23-35 (2011).

  80. Monotonicity and uniqueness of a 3D transonic shock solution in a conic nozzle with variable end pressure, (with J. Li, H. Yin), Pacific J. Math., Vol. 254, No. 1, 129-171 (2011).

  81. Pointwise Stability of Contact Discontinuity for Viscous Conservation Laws with General Perturbations, (with H.H. Zeng), Comm. PDE, Vol. 35, No. 7, 1326-1354 (2010).

  82. Boundary layers in incompressible Navier-Stokes equations with Navier-boundary conditions for the vanishing viscosity limit, (with X. P. Wang & Y. G. Wang), Comm. Math. Sci., Vol. 8, No. 4, 965-998 (2010).

  83. The existence and monotonicity of a three-dimensional transonic shock in a finite nozzle with axisymmetric exit pressure, (with J. Li, H. Yin), Pacific J. Math. 247 (2010), No. 1, 109-161.

  84. Convergence to rarefaction waves for the nonlinear Boltzmann equation and compressible Navier-Stokes equations, (with H. H. Zeng), JDE, 249, no. 4, 827-871 (2010).

  85. Global subsonic and subsonic-sonic flows through infinitely long axially-symmetric nozzles, (with C. Xie), JDE, 248, No. 11, 2657-2683 (2010).

  86. The latest trend in modern mathematics (Chinese), Pure Appl. Math., 26, No. 1, 1-2 (2010).

  87. A blow-up criterion for classical solutions to the compressible Navier-Stokes equations, (with X. D. Huang), Science in China Mathematics, Vol. 53, No. 3, 671-686 (2010).

  88. Existence of global steady subsonic Euler flows through infinitely long nozzles, (with C. Xie), SIAM J. Math. Anal., 42, No. 2, 751-784 (2010).

  89. On transonic shocks in a conic divergent nozzle with axi-symmetric exit pressure, (with J. Li & H.C. Yin), JDE, 248 (2010), 423-469.

  90. Existence of solutions for three dimensional stationary incompressible Euler equations with nonvanishing vorticity, (with C.L. Tang), Chin. Ann. Math. 30B(6), (2009), 803-830.

  91. Vanishing viscosity limit for the 3D magneto-hydrodynamics with a slip boundary condition, (with Y.L. Xiao & J.H. Wu), J. Funct. Anal., Vol. 257, No. 11, 3375-3394 (2009).

  92. Smooth Approximations and exact solutions of the 3D steady Axisymmetric Euler Equations, (with Q.S. Jiu), Comm. Math. Phys. 287 (2009), 323-349.

  93. On the self-similar solutions of the magneto-hydro-dynamic equations, (with C. He), Acta Math. Sci. Ser. B Engl. Ed. 29 (2009), no. 3, 583-598.

  94. On transonic shocks in a nozzle with variable end pressure, (with J. Li, H. C. Yin), Comm. Math. Phys., Vol. 291, no 1, 111-150 (2009).

  95. Transonic Shock problem for the Euler system in a nozzle, (with W. Yan, H. C. Yin), Arch. Rat. Mech. Anal., Vol. 194, no. 1, 1-47 (2009).

  96. A Free Boundary Value Problem for the Full Euler System and 2-D Transonic Shock in a Large Variable Nozzle, (with J. Li & H.C. Yin), Math. Res. Lett. 16, No. 5, 777-796 (2009).

  97. Spherically symmetric isentropic compressible flows with density-dependent viscosity coefficients, (with Z.H. Guo, & Q.S. Jiu), SIAM J. Math. Anal. 39 (2008), No. 5, 1402-1427.

  98. Three-dimensional transonic shocks in a nozzle, (with H.C. Yin), Pacific J. Math. 236 (2008), No. 1, 139-193.

  99. The Cauchy problem for 1D compressible flows with density-dependent viscosity coefficients, (with Q.S. Jiu), Kinet. Relat. Models 1 (2008), No. 2, 313-330.

  100. Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations, (with H.L. Li & J. Li), Comm. Math. Phys. 281 (2008), No. 2, 401-444.

  101. The transonic shock in a nozzle, 2-D and 3-D complete Euler systems, (with H.C. Yin), J. Differential Equations 245 (2008), No. 4, 1014-1085.

  102. Contact discontinuity with general perturbations for gas motions, (with F.M. Huang & T. Yang), Adv. Math. 219 (2008), No. 4, 1246-1297.

  103. On Strong Convergence to 3D steady vortex sheets, (with Q. S. Jiu), JDE 239 (2007), 448-470.

  104. Global Subsonic and Subsonic-Sonic Flows through Infinitely Long Nozzles, (with C. J. Xie), Indiana Univ. Math. J., 56 (2007), No. 6, 2991-3023.

  105. On the vanishing viscosity limit for the 3D Navier-Stokes equations with a slip boundary condition, (with Y.L. Xiao), Comm. Pure Appl. Math., 60 (2007), No. 7, 1027-1055.

  106. Navier-Stokes approximations to 2D vortex sheets in half plane, (with D.J. Niu & Q.S. Jiu), Methods Appl. Anal. 14 (2007), No. 3, 263-271.

  107. Some uniform estimates and blow-up behavior of global strong solutions to the Stokes approximation equations for two-dimensional compressible flows, (with J. Li), J. Diff. Eqns., 221 (2006), 275-308.

  108. Global multi-dimensional shock wave for the steady supersonic flow past a three-dimensional curved cone, (with H. C. Yin), Analysis and Applications, Vol. 4, No. 2 (2006), 101-132.

  109. Vacuum State for Spherically Symmetric Solutions of the Compressible Navier-Stokes Equations, (with H. J. Yuan), JHDE 3 (2006), no. 3, 403-442.

  110. Vortex sheets with reflection symmetry in exterior domains, (with M. C. Lopes F. & H. J. N. Lopes), J. Diff. Eqns. 229 (2006), no. 1, 154-171.

  111. Stability of Contact Discontinuities for the 1-D Compressible Navier-Stokes Equations, (with F. M. Huang, A. Matzumura), Arch. Rat. Mech. Anal., 179 (2006), No. 1, 55-77.

  112. Convergence to Equilibria and Blow-up Behavior of Global Strong Solutions to the Stokes Approximation Equations for Two-dimensional Compressible Flows with Large Data, (with F. M. Huang & J. Li), J. Math. Pures. Appl. (9) 86 (2006), no. 6, 471-491.

  113. On strong convergence to 3-D axisymmetric vortex sheets, (with Q-S. Jiu), J. Diff. Eqns., 223 (2006), No. 1, 33-50.

  114. Quasineutral Limit of Drift diffusion models for semiconductors: The case of general Sign-changing doping profile, (with S. Wang & P. Markowich), SIAM J. of Math. Anal., 37 (2006), No. 6, 1854-1889.

  115. Zero viscous limit of the linearized Navier-Stokes equations with highly oscillatoryforce in the half-plane, (with Y. G. Wang), SIAM J. Math. Anal., Vol. 37 (2006), No. 4, 1256-1298.

  116. Transonic shocks in a nozzle I, 2-D case, (with H. Yin), Comm. Pure Appl. Math., 58 (2005), No. 8, 999-1050.

  117. Partial regularity of suitable weak solutions to the Incompressible Magnitohychodynamic equations, (with C. He), J. Functional Anal., 227 (2005), 113-152.

  118. On the regularity of solutions to the Magneto-Hydrodynamic equations, (with Cheng He), JDE, 213 (2005), No. 2, 235-254.

  119. Global weak solutions to 1D Compressible Isentropic Navier-Stokes Equations with Density-Dependent Viscosity, (with S. Jiang and P. Zhang), Methods Applications Analysis, Vol. 12, No. 3, 239-252 (2005).

  120. On the global existence of solutions of Prandtl's system, (with L. Q. Zhang), Advances in Math., 181 (2004), 88-133.

  121. Stability and existence of multidimensional subsonic phase transitions, (with Y. G. Wang), Acta Mathematicae Applicatae Sinica, English Series, Vol. 19, No. 4 (2003), 529-558.

  122. Viscous approximation and decay rate of maximal vorticity function for 3-D axi-symmetric Euler equations, Acta. Math. Sinica, English Series, Vol. 20, No. 3, 385-404 (2003).

  123. Fractional rate of convergence for viscous approximation to nonconvex conservation laws, (with T. Tang & Z-H. Tong), SIAM J. Math. Anal., Vol. 35, No. 1 (2003), 98-122.

  124. On the uniqueness and large time behavior of the weak solutions to a shallow water equation, (with P. Zhang), Comm. PDE, Vol. 27, (2002), 1815-1844.

  125. Global shock waves for the supersonic flow past a perturbed cone, (with S. Chen and H. Yin), Commun. Math. Phys. Vol. 228, 47-84 (2002).

  126. Initial-Boundary value problem to systems of conservation laws with relaxation, (with W.-Q., Xu), Quart. Appl. Math. 60 (2002), No. 2, 251-281.

  127. Homogeneity criterion on the Navier-Stokes equations in the whole space, (with Z.M. Chen), J. Math. Fluid Mech., 3(2001), 152-182.

  128. Existence of Vortex sheets with reflection symmetry in two space dimensions, (with H. Lopes and M. Filho), Arch. Rat. Mech. Anal., 158 (2001), 235-257.

  129. Convergence of point vortex method for 2-D discontinuous Euler flows, (with J.G. Liu), Math. Computation AMS, 70 (2001), 595-606.

  130. On the decay properties of solutions to the nonstationary Navier-Stokes equations in R3, (with Cheng He), Proceedings of Royal Society of Edinburgh Section A: Mathematics, Royal Society, 131A, (2001), 597-619.

  131. Interface behavior of compressible Navier-Stokes Equations, (with T. Luo and T. Yang), SIAM J. Applied Math., 31(2000), No. 6. 1175-1191.

  132. Stiff well-possedness and asymptotic convergence for a class of linear relaxation systems in a quarter plane, (with W.Q. Xu), J. Differential Equations, 167 (2000), 388-437.

  133. Weighted estimates for the non-stationary Navier-Stokes Equations in the exterior domains, (with Cheng He), Methods and Applications of Analysis, Vol. 7, No. 3 (2000), 443-458.

  134. On weak solutions to a shallow water equation, (with P. Zhang), Comm. Pure Applied Math., Vol. LIII, 1411-1433 (2000).

  135. Convergence of a Galerkin method for 2-D discontinuous Euler flows, (with J. G. Liu), Comm. Pure Applied Math., 53 (2000), No 6. 786-798.

  136. Relaxation schemes for curvature-dependent front propagation, (with J. Shi and M. Katsoulakis), Comm. Pure Appl. Math., Vol. 52 (1999), No. 12, 1587-1615.

  137. Large time behavior of solutions to a hydrodynamic model for semiconductors, (with T. Luo, and R. Natalini). SIAM J. Applied Math., Vol. 59, No. 3 (1999), 810-830.

  138. Zero viscosity limit of the linearized Navier-Stokes equations for a compressible viscous fluids in the half plan, (with T. Yanagisawa), Comm. Pure Appl. Math., Vol. LII, (1999), 497-541.

  139. Gradient estimates for the 3D incompressible Navier-Stokes equations, (with G. Tian), Comm. Analysis and Geometry, Vol. 7, No. 2 (1999), 221-257.

  140. On the blow-up of smooth solutions to the compressible Navier-Stokes equations with compact density, Comm. Pure Appl. Math., 51 (1998) 229-240.

  141. Vacuum states for compressible flows, (with T.-P. Liu and T. Yang), Disc. Cont. Dynamical Systems, 4 (1998), 1-32.

  142. Asymptotic limit of the initial boundary value problems for conservations with relaxational extensions, (with W.-C. Wang), Comm. Pure Appl. Math., 51 (1998) 505-535.

  143. Fluid-dynamic limit for the centered rarefaction waves of the Broadwell equations, (with W. C. Wang), Journal Differential Equations, Vol. 150 (1998), 438-461.

  144. Viscous boundary layers and their stability (I), J. Part. Diff. Eqs., 11 (1998), 74-124.

  145. Numerical passage from systems of conservation laws to Hamilton-Jacobi equations, (with J. Shi), SIAM J. Numer. Anal., Vol. 35, No. 6 (1998) 2385-2404.

  146. One-point singular solutions to 3D Navier-Stokes equations, (with G. Tian), Top. Meth. Nonlinear Analysis, Vol. 2 (1998), 221-237.

  147. Shock and boundary layer behavior of solutions to the Broadwell equation in the fluid-dynamic limit, AMS/IP Studies in Advanced Mathematics, 3 (1997) 455-468.

  148. Initial-boundary value problems for conservation laws, (with P. Kan and M. Santos), Comm. Math. Physics, 186 (1997) 701-730.

  149. Nonlinear stability of shock fronts for a relaxation system in several space dimensions, (with T. Luo), J. Diff. Eqs., 139 (1997) 365-408.

  150. Pointwise decay to contact discontinuities for systems of viscous conservation laws, (with T.-P. Liu), Asian J. Math., 1 (1997), 34-84.

  151. Boundary layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation, (with J. G. Liu), Arch. Rat. Mech. Anal., 135 (1996) 61-105.

  152. Kinetic and viscous boundary layers for Broadwell equations, (with J.-G. Liu), Transport Theory and Statistic Physics, 25 (1996) 447-462.

  153. Initial boundary value problem for a class of quadratic systems of conservation laws, (with P. Kan and M. Santos), Matematica Contemporanea, 11 (1996) 1-32.

  154. The relaxation schemes for systems of conservation laws in arbitrary dimensions, (with S. Jin), Comm. Pure Appl. Math., 48 (1995) 235-276.

  155. Convergence of vortex methods for weak solutions to the 2-D Euler equations with vortex sheets data, (with J.-G. Liu), Comm. Pure Appl. Math., 48 (1995) 611-628.

  156. Uniqueness via the adjoint problem for systems of conservation laws, (with LeFloch), Comm. Pure Appl. Math., 46 (1993) 1499-1533.

  157. Nonlinear stability of viscous shock waves, (with A. Szepessy), Arch. Rat. Mech. Anal., 122 (1993), 53-103.

  158. L1 -stability of stationary discrete shocks, (with J.-G. Liu) Math. Comp., 60 (1993) 233-244.

  159. Zero dissipation limit to rarefaction waves for one-dimensional Navier-Stokes equations for compressible isentropic gases, Comm. Pure Appl. Math., 46 (1993) 621-665.

  160. Nonlinear stability of discrete shocks for systems of conservation laws, (with J.-G. Liu), Arch. Rat. Mech. Anal., 125 (1993), 217-256.

  161. Stability of viscous shock waves associated with a system of non-strictly hyperbolic conservation laws, (with T.-P. Liu), Comm. Pure Appl. Math., 45 (1992) 361-388.

  162. On the linearized stability of viscous shock profiles for systems of conservation laws, J. Diff. Eqs., 100 (1992) 119-136.

  163. Viscous limits to piecewise smooth solutions of systems of conservation laws, (with J. Goodman) Arch. Rat. Mech. Anal., 121 (1992) 235-265.

  164. The fluid-dynamic limit of the Broadwell model of the nonlinear Boltzmann equation in the presence of shocks, Comm. Pure Appl. Math., 44, (1991) 679-713.

  165. The fluid-dynamic limit of the Broadwell equation, SIAM Volume on Viscous and Numerical Approximations of Shock Waves, (1991) 237-252.

  166. Asymptotic stability of planar rarefaction waves for viscous conservation laws in several dimensions, Transactions of AMS, 319 (1990) 805-820.

  167. Instability of rarefaction shocks in systems of conservation laws, (with J. Smoller, B. Temple), Arch. Rat. Mech. Anal., 112 (1990) 63-81.

  168. Asymptotic stability of rarefaction waves for 2 x 2 viscous hyperbolic conservation laws --- the two-mode case, J. Diff. Eqs., 78 (1989) 191-219.

  169. Over-compressive shock waves, Proc. Workshop on Mixed Type Equations and Phase Transition, (with T.-P. Liu), IMA, Vol. 27, (1989).

  170. Asymptotic stability of rarefaction waves for 2 x 2 viscous hyperbolic conservation laws, J. Diff. Eqs., 73 (1988) 45-77.

  171. Nonlinear stability of rarefaction waves for compressible Navier-Stokes equations, (with T.-P. Liu), Comm. Math. Phys., 118 (1988) 451-465.

  172. On the asymptotic behavior of solutions of a reaction-diffusion system, a two-predator--one-prey model, (with L. Hsiao and Y. Su), SIAM J. Math. Anal., 18 (1987) 647-669.

  173. The tubular catalysts reactor and the Robin problem, Acta Math. Appl. Sinica 3 (1987).


Refereed Conference papers (total: 7):

  1. Some regularity criteria on suitable weak solutions of the 3-D incompressible axisymmetric Navier-Stokes equations, (with Q-S. Jiu), Vol. 2, New Studies in Advanced Mathematics, IP (2003), 119-140.

  2. On Multi-Dimensional Compressible Navier-Stokes Equations, International Press, Frontiers of Mathematical Sciences, 439-454 (2011).

  3. Analysis of some singular solutions in fluid dynamics, Proceedings of the International Congress of Mathematicians (2002), Vol. III, Invited Lectures, 851-860.

  4. On the behavior of solutions to the compressible Navier-Stokes equations, Studies in Advanced Mathematics, Vol. 20, Proc. of ICCM98, (2001), 159-170.

  5. On the convergence of vortex methods for weak solutions to the 2-D Euler equations, (with J.-G. Liu), Proceedings of the Fifth International Conference on Hyperbolic Problems: Theory, Numerics, and Applications, edited by Glimm etc., World Scientific, (1996) 398-404.

  6. The relaxation scheme, (with J. Shi), Proceeding of the Fifth International Conference on Hyperbolic Problems: Theory, Numerics, and Applications, edited by Glimm, etc., World Scientific, (1996), 361-367.

  7. On nonlinear stability of contact discontinuities, Proceeding of the 5th International Conference on Hyperbolic Problems: Theory, Numerics, Applications, edited by Glimm, etc. World Scientific, (1996) 249-257.


Journal Papers to appear/under review (total: 4):

  1. Existence and stability of cylindrical transonic shock solutions under three dimensional perturbations, (with Shangkun Weng), IMS Preprint Series 2023-01 (233) (2023).

  2. Global smooth solutions to the 2D isentropic and irrotational Chaplygin gases with a class of large initial data (with Bingbing Ding, Huicheng Yin), arXiv:2204.05017 (2022).

  3. Global Well-posedness and Regularity of Weak Solutions to the Prandtl’s System (with Liqun Zhang, Junning Zhao), submitted to SIMA, arXiv:2204.05017 (2022).

  4. Global existence of weak solutions to the barotropic compressible Navier-Stokes flows with degenerate viscosities, (with Jing Li), preprint, arXiv: 1504.06826 (2015).


Chapters of Books (total: 4):

  1. Global Existence of Regular Solutions with Large Oscillations and Vacuum for Compressible Flows, (with J. Li), Springer Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, Chapter 38, 2018.

  2. Finite Time Blow Up of Regular Solutions for Compressible Flows, (with X. D. Huang), Springer Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, Chapter 40, 2018.

  3. Theory of viscous conservation laws, AMS/IP Studies in Advanced Mathematics, Vol. 15 (2000), 141-193.

  4. Some open problems in partial differential equations arising from fluid dynamics, Current Development of Mathematics (1997), Edited by Batt. etc., International Press, 231-277.


Books Edited (total: 2):

  1. Proceedings of The Third International Congress of Chinese Mathematicians (2004), Part 1, 2, (with K. S. Lau and S. T. Yau), AMS/IP Stud. in Adv. Math., 42, 2008.

  2. Some Current Topics in Nonlinear Conservation Laws, (edited with L. Hsiao), Studies in Advanced Mathematics, AMS/IP, Vol. 15. 2000.


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KEYNOTE SPEECHES/ DISTINGUISHED LECTURES (SINCE 1992; Total: 164)

全国偏微分方程理论与应用研究学术会议, SYSU, Guangzhou, China, 1/2024

Yau Conference 2024 - A Conference in Celebration of Professor Shing-Tung Yau, UNIST, South Korea, 1/2024

首届数学物理与几何中的偏微分方程学术研讨会, Zhejiang Normal University, Jinhua, China, 1/2024

The 2023 Annual International Congress of Chinese Mathematicians (ICCM2023), Shanghai, China, 1/2024

2023 年非线性偏微分方程研讨会, Beijing Normal University, Beijing, China, 12/2023

Master Talk of 10th Anniversary of TSIMF, Sanya, Hainan, 12/2023

Australia-China Joint Conference on PDEs, Sydney, Australia, 12/2023Zhouping

甬江PDE 前沿论坛, Zhejiang, Ningbo, China 12/2023

非綫性偏微分方程新進展―西安2023 研讨会, Xian Jiaotong University, Xian, China, 11/2023

边界层及相关主题数学理论研讨会, Shanghai Jiao Tong University, Shanghai, China, 10/2023

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INVITED PRESENTATIONS FOR CONFERENCE AND WORKSHOPS (SINCE 1992, Total: 210)

Workshop on the Recent Progress of Mathematical Theory for Fluid Mechanics, Jiangsu (online), 4/2021

ICCM 2020 Online Series of Conferences on Applied Math, Shing-Tung Yau Center of Southeast University, China, 10/2020

Program on “Optimal Transportation Problems, PDEs and Their Applications in Image Processing”, Nanjing, China, 08/2020

Tianyuan Symposium and International Conference on Frontier Basic Theory of Fluid Computing and High-efficiency-number Methods, Xian, China, 07/2020

Analysis and Geometry Symposium and Science in China: Mathematics, Harbin, China, 01/2020

Workshop on Nonlinear PDEs and Related Topics, Singapore, 12/2019

Opening Ceremony of International Applied Mathematics Center at Greater Bay Area and Workshop on Applied Mathematics, Guangzhou, China, 12/2019

Workshop on nonlinear PDE theory and applications, Shanghai, China, 12/2019

International Conference on Partial Differential Equations in Fluids, Guangzhou, China, 11/2019

International workshop on Modeling, applied analysis and computation of fluids, Shenzhen, China, 10/2019

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CONFERENCE ORGANIZATION (SINCE 1997)

Chairman of Scientific Committee, Annual National Summer School on PDEs and Related International Workshops, China, since 2003

Chair & Organizing Committee, International Conference on Partial Differential Equations in Fluids, Guangzhou, China, 11/2019

Organizing Committee, Quantum and Kinetic Problems: Modeling, Analysis Numerics and Applications, NUS, Singapore, 09/2019-03/2020

Programme Committee Chair, International Workshop on PDEs, CUHK, Hong Kong, 05/2019

Programme Committee Chair, IMS Workshop on PDEs, CUHK, Hong Kong, 01/2019

Scientific Committee, Analysis and Partial Differential Equations Workshop, Center for Nonlinear Studies and School of Mathematics, Northwest University, Xian, China, 06/2018

Programme Committee Member, Workshop on Fractal Geometry and Related Topics, CUHK, Hong Kong, 05/2018

Programme Committee Chair, Workshop on Compressible Navier-Stokes Systems and Related Problems (I), CUHK, Hong Kong, 03/2018

Programme Committee Chair, Workshop on Compressible Navier-Stokes Systems and Related Problems (II), CUHK, Hong Kong, 03/2018

Programme Committee Chair, IMS PDE Day (I), CUHK, Hong Kong, 02/2018

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