研究人员 Faculty

李进开(Jinkai LI)

学历/职称:

研究员

研究方向:

非线性偏微分方程(流体动力学,大气海洋)

联系方式:

jklimath@m.scnu.edu.cn; jklimath@hotmail.com

  • 基本信息
    • 华南师范大学华南数学应用与交叉研究中心研究员,教授,博士生导师,2018年入选国家海外高层次人才引进计划青年项目,曾获得“2020世界华人数学家联盟最佳论文奖”金奖(2020 ICCM Best Paper Award)以及“第二届中国科协优秀科技论文”奖。2013年博士毕业于香港中文大学数学科学研究所,导师为辛周平教授。2013至2016于以色列威兹曼科学研究所(Weizmann Institute of Sciences)从事博士后研究工作,合作导师为Edriss S. Titi教授。2016至2018在香港中文大学数学系任研究助理教授。2018年其至今在华南师范大学华南数学应用与交叉研究中心工作。主要从事流体动力学方程方面的研究,主要包括大气海洋动力学偏微分方程(以Primitive Equatgions为代表)、Navier-Stokes方程组、复杂流体等。目前已在包括CPAM, Adv. Math, JFA, ARMA, CPDE, SIMA等国际学术期刊上发表SCI论文30余篇,主持国家自然科学基金面上项目1项,香港研究资助局面上项目1项,广东省基础与应用基础研究基金自然科学基金面上项目1项,广东省基础与应用基础研究基金粤港澳应用数学中心项目1项。

  • 教育背景
    • 2010/082013/07:香港中文大学   博士   导师:辛周平 教授 

    • 2006/082008/07:吉林大学          硕士   导师:尹景学 教授

    • 2002/082006/07:吉林大学          本科  

    • Aug 2010–Jul 2013:  The Chinese University of Hong Kong    PhD    Advisor: Prof. Zhouping Xin

    • Aug 2006–Jul 2008:  Jilin University   Mph    Advisor: Prof. Jingxue Yin

    • Aug 2002–Jul 2006:  Jilin University    Bachelor of Science

  • 工作经历
    • 2018/07--至今:       华南师范大学         教授

    • 2016/08--2018/06: 香港中文大学         研究助理教授

    • 2013/08--2013/07: Weizmann研究所  博士后

    • July 2018 – present:  South China Normal University    Professor

    • Aug 2016 – July 2018:  The Chinese University of Hong Kong    Research Assistant Professor

    • Aug 2013 – July 2016:   Weizmann Institute of Science     Postdoctoral Fellow   (Mentor: Prof. Edriss S. Titi)

  • 研究领域
    • 大气海洋动力学方程(Primitive Equations)     

    • 流体动力学方程(Navier-Stokes Equations)  

  • 科研项目
    • 2020.01.01--2023.12.31:关于具真空情形可压缩流体熵的有界性的研究;国家自然科学基金面上项目11971009;53万;主持

    • 2020.01.01--2022.12.31:大气海洋多尺度模型及其数学分析;广东省基础与应用基础研究基金粤港澳中心项目2020B1515310002;50万;参与

    • 2020.01.01--2022.12.31:复杂成分材料智能制造中的多相(流)界面问题;广东省基础与应用基础研究基金粤港澳中心项目2020B1515310005;30万;主持

    • 2019.10.01--2022.09.30:无热传导情形大气海洋偏微分方程组的适定性问题;广东省基础与应用基础研究基金自然科学基金面上项目2019A1515011621;10万;主持

    • 2019.01.01--2022.12.31:磁流体力学方程组的稳定性和不稳定性研究;国家自然科学基金面上项目11871005;53万;参与

    • 2018.01.01--2021.12.31:具退化或其他奇异性非线性扩散方程的定性理论;国家自然科学基金面上项目11771156;48万;参与

    • 2017.09.01--2020.08.01: General Research Fund from RGC Hong Kong (PI, project no. 14302917), HK$ 473,351. Title: Weak and Strong Solutions to the Primitive Equations with Full or Horizontal Viscosity but No Diffusivity

    • 2017.01.01--2017.12.01: Direct Grant 2016/2017 from CUHK (PI, Project Code: 4053216), HK$100,000. Title: Existence and Uniqueness of Solutions to Primitive Equations without Diffusivity

  • 获得荣誉
    • Israel Council for Higher Education (VATAT) Postdoctoral Fellowship  (2013-2016)

    • Best paper of Mathematical Models and Methods in Applied Sciences (M3AS) in 2016

    • 《第二届中国科协优秀科技论文》2017

    • 《数学物理学报》优秀论文2016

    •  Simons Visiting Professor (SVP) to Oberwolfach

    • 国家海外高层次人才引进计划”青年项目

    • 2020世界华人数学家联盟最佳论文奖金奖(2020 ICCM Best Paper Award)


  • 教学经验
    • Navier-Stokes Equations: Fall 2020

    • Sobolev Spaces and L^2 Theory of PDEs: Fall 2019

    • MATH3270B Ordinary Differential Equations: Summer 2018

    • MATH 3270A Ordinary Differential Equations: Fall 2016

  • 论文发布
    1. Cao, Chongsheng; Li, Jinkai; Titi, Edriss S.: Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity. Phys. D 412 (2020), 132606

    2. Li, Jinkai: Global small solutions of heat conductive compressible Navier-Stokes equations with vacuum: smallness on scaling invariant quantity. Arch. Rational Mech. Anal. 237 (2020) 899–919  

    3. Gong, Huajun; Li, Jinkai; Liu, Xiangao; Zhang, Xiaotao: Local well-posedness of isentropic compressible Navier-Stokes equations with vacuum. Commun. Math. Sci. 18 (2020) (7) 1891--1909

    4. Hittmeir, Sabine; Klein, Rupert; Li, Jinkai; Titi, Edriss S.: Global Well-posedness for the Primitive Equations Coupled to Nonlinear Moisture Dynamics with Phase Changes. Nonlinearity 33 (2020) 3206–3236

    5. Li, Jinkai; Global well-posedness of non-heat conductive compressible Navier-Stokes equations in 1D. Nonlinearity 33 (2020), 2181–2210

    6. Li, Jinkai; Xin, Zhouping; Entropy bounded solutions to the one-dimensional compressible Navier-Stokes equations with zero heat conduction and far field vacuum. Adv. Math. 361(2020), 106923. 

    7. Bian, DongfenLi, Jinkai Finite time blow up of compressible Navier-Stokes equations on half space or outside a fixed ball. J. Differential Equations 267 (2019), no. 12, 7047–7063. 

    8. Li, Jinkai Global well-posedness of the one-dimensional compressible Navier-Stokes equations with constant heat conductivity and nonnegative density. SIAM J. Math. Anal. 51(2019), no. 5, 3666–3693. 

    9. Li, JinkaiTiti, Edriss S. The primitive equations as the small aspect ratio limit of the Navier-Stokes equations: rigorous justification of the hydrostatic approximation. J. Math. Pures Appl. (9) 124 (2019), 30–58.

    10. Li, JinkaiTiti, Edriss S. Recent advances concerning certain class of geophysical flows. Handbook of mathematical analysis in mechanics of viscous fluids, 933–971, Springer, Cham,2018. 

    11. Li, JinkaiXu, ZhonghaiZhang, Jianwen Global existence of classical solutions with large oscillations and vacuum to the three-dimensional compressible nematic liquid crystal flows.J. Math. Fluid Mech. 20 (2018), no. 4, 2105–2145.

    12. Gong, HuajunHuang, TaoLi, Jinkai Nonuniqueness of nematic liquid crystal flows in dimension three. J. Differential Equations 263 (2017), no. 12, 8630–8648.

    13. Hittmeir, SabineKlein, RupertLi, JinkaiTiti, Edriss S. Global well-posedness for passively transported nonlinear moisture dynamics with phase changes. Nonlinearity 30 (2017), no. 10, 3676–3718.

    14. Li, Jinkai Local existence and uniqueness of strong solutions to the Navier-Stokes equations with nonnegative density. J. Differential Equations 263 (2017), no. 10, 6512–6536.

    15. Cao, ChongshengLi, JinkaiTiti, Edriss S. Strong solutions to the 3D primitive equations with only horizontal dissipation: near H1 initial data. J. Funct. Anal. 272 (2017), no. 11,4606–4641.

    16. Li, JinkaiTiti, Edriss S. Existence and uniqueness of weak solutions to viscous primitive equations for a certain class of discontinuous initial data. SIAM J. Math. Anal. 49 (2017), no. 1, 1–28.

    17. Gong, HuajunLi, JinkaiXu, Chen Local well-posedness to inhomogeneous Ericksen-Leslie system with general Leslie stress tensor. Z. Angew. Math. Phys. 68 (2017), no. 1, Art. 17, 23 pp. 

    18. Gong, HuajunLi, JinkaiXu, Chen Local well-posedness of strong solutions to density-dependent liquid crystal system. Nonlinear Anal. 147 (2016), 26–44.

    19. Li, JinkaiTiti, Edriss S. A tropical atmosphere model with moisture: global well-posedness and relaxation limit. Nonlinearity 29 (2016), no. 9, 2674–2714.

    20. Cao, ChongshengLi, JinkaiTiti, Edriss S. Global well-posedness of the three-dimensional primitive equations with only horizontal viscosity and diffusion. Comm. Pure Appl. Math.69 (2016), no. 8, 1492–1531.

    21. Li, JinkaiXin, Zhouping Global existence of weak solutions to the non-isothermal nematic liquid crystals in 2D. Acta Math. Sci. Ser. B (Engl. Ed.) 36 (2016), no. 4, 973–1014.

    22. Li, JinkaiTiti, Edriss Global well-posedness of strong solutions to a tropical climate model. Discrete Contin. Dyn. Syst. 36 (2016), no. 8, 4495–4516.

    23. Li, JinkaiTiti, Edriss S. Global well-posedness of the 2D Boussinesq equations with vertical dissipation. Arch. Ration. Mech. Anal. 220 (2016), no. 3, 983–1001.

    24. Li, JinkaiTiti, Edriss S.Xin, Zhouping On the uniqueness of weak solutions to the Ericksen-Leslie liquid crystal model in R2Math. Models Methods Appl. Sci. 26 (2016), no. 4, 803–822.

    25. Fan, JishanLi, Jinkai A logarithmic regularity criterion for the 3D generalized MHD system. Math. Methods Appl. Sci. 38 (2015), no. 18, 5279–5283.

    26. Li, Jinkai Global strong solutions to the inhomogeneous incompressible nematic liquid crystal flow. Methods Appl. Anal. 22 (2015), no. 2, 201–220.

    27. Fan, JishanLi, Jinkai Regularity criteria for the strong solutions to the Ericksen-Leslie system in R3J. Math. Anal. Appl. 425 (2015), no. 2, 695–703.

    28. Cao, ChongshengLi, JinkaiTiti, Edriss S. Global well-posedness of strong solutions to the 3D primitive equations with horizontal eddy diffusivity. J. Differential Equations 257(2014), no. 11, 4108–4132.

    29. Ma, WenyaGong, HuajunLi, Jinkai Global strong solutions to incompressible Ericksen-Leslie system in R3Nonlinear Anal. 109 (2014), 230–235.

    30. Cao, ChongshengLi, JinkaiTiti, Edriss S. Local and global well-posedness of strong solutions to the 3D primitive equations with vertical eddy diffusivity. Arch. Ration. Mech. Anal.214 (2014), no. 1, 35–76.

    31. Hong, Min-ChunLi, JinkaiXin, Zhouping Blow-up criteria of strong solutions to the Ericksen-Leslie system in R3Comm. Partial Differential Equations 39 (2014), no. 7, 1284–1328.

    32. Gong, HuajunLi, Jinkai Global existence of strong solutions to incompressible MHD. Commun. Pure Appl. Anal. 13 (2014), no. 3, 1337–1345.

    33. Li, Jinkai Global strong and weak solutions to inhomogeneous nematic liquid crystal flow in two dimensions. Nonlinear Anal. 99 (2014), 80–94.

    34. Yin, JingxueLi, JinkaiKe, Yuanyuan Existence of positive solutions for the p(x)-Laplacian equation. Rocky Mountain J. Math. 42 (2012), no. 5, 1675–1758.  

    35. Li, JinkaiYin, JingxueKe, Yuanyuan Existence of positive solutions for the p-Laplacian with p-gradient term. J. Math. Anal. Appl. 383 (2011), no. 1, 147–158.

    36. Yin, JingxueLi, JinkaiKe, Yuanyuan Existence of solutions for the p-Laplacian with critical Sobolev exponent and convection. Appl. Anal. 89 (2010), no. 10, 1575–1590.