李进开（Jinkai LI） - 专职教师 - 华南师范大学华南数学应用与交叉研究中心

教育背景
- 2010/08–2013/07：香港中文大学博士导师：辛周平教授
- 2006/08–2008/07：吉林大学硕士导师：尹景学教授
- 2002/08–2006/07：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
- 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
论文发布
1. Li, Jinkai: Global small solutions of heat conductive compressible Navier-Stokes equations with vacuum: smallness on scaling invariant quantity; Arch. Ration. Mech. Anal. (2020 accepted) http://statics.scnu.edu.cn/pics//2020/0505/1588677338922601.pdf
2. Gong, Huajun; Li, Jinkai; Liu, Xiangao; Zhang, Xiaotao: Local well-posedness of isentropic compressible Navier-Stokes equations with vacuum. Commun. Math. Sci. (2020 accepted)
3. 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 (2020 accepted)
4. Li, Jinkai; Global well-posedness of non-heat conductive compressible Navier-Stokes equations in 1D. Nonlinearity 33 (2020), 2181–2210
5. 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.
6. Bian, Dongfen; Li, 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.
7. 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.
8. Li, Jinkai; Titi, 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.
9. Li, Jinkai; Titi, Edriss S. Recent advances concerning certain class of geophysical flows. Handbook of mathematical analysis in mechanics of viscous fluids, 933–971, Springer, Cham,2018.
10. Li, Jinkai; Xu, Zhonghai; Zhang, 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.
11. Gong, Huajun; Huang, Tao; Li, Jinkai Nonuniqueness of nematic liquid crystal flows in dimension three. J. Differential Equations 263 (2017), no. 12, 8630–8648.
12. Hittmeir, Sabine; Klein, Rupert; Li, Jinkai; Titi, Edriss S. Global well-posedness for passively transported nonlinear moisture dynamics with phase changes. Nonlinearity 30 (2017), no. 10, 3676–3718.
13. 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.
14. Cao, Chongsheng; Li, Jinkai; Titi, 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.
15. Li, Jinkai; Titi, 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.
16. Gong, Huajun; Li, Jinkai; Xu, 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.
17. Gong, Huajun; Li, Jinkai; Xu, Chen Local well-posedness of strong solutions to density-dependent liquid crystal system. Nonlinear Anal. 147 (2016), 26–44.
18. Li, Jinkai; Titi, Edriss S. A tropical atmosphere model with moisture: global well-posedness and relaxation limit. Nonlinearity 29 (2016), no. 9, 2674–2714.
19. Cao, Chongsheng; Li, Jinkai; Titi, 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.
20. Li, Jinkai; Xin, 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.
21. Li, Jinkai; Titi, Edriss Global well-posedness of strong solutions to a tropical climate model. Discrete Contin. Dyn. Syst. 36 (2016), no. 8, 4495–4516.
22. Li, Jinkai; Titi, Edriss S. Global well-posedness of the 2D Boussinesq equations with vertical dissipation. Arch. Ration. Mech. Anal. 220 (2016), no. 3, 983–1001.
23. Li, Jinkai; Titi, Edriss S.; Xin, Zhouping On the uniqueness of weak solutions to the Ericksen-Leslie liquid crystal model in R2. Math. Models Methods Appl. Sci. 26 (2016), no. 4, 803–822.
24. Fan, Jishan; Li, Jinkai A logarithmic regularity criterion for the 3D generalized MHD system. Math. Methods Appl. Sci. 38 (2015), no. 18, 5279–5283.
25. Li, Jinkai Global strong solutions to the inhomogeneous incompressible nematic liquid crystal flow. Methods Appl. Anal. 22 (2015), no. 2, 201–220.
26. Fan, Jishan; Li, Jinkai Regularity criteria for the strong solutions to the Ericksen-Leslie system in R3. J. Math. Anal. Appl. 425 (2015), no. 2, 695–703.
27. Cao, Chongsheng; Li, Jinkai; Titi, 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.
28. Ma, Wenya; Gong, Huajun; Li, Jinkai Global strong solutions to incompressible Ericksen-Leslie system in R3. Nonlinear Anal. 109 (2014), 230–235.
29. Cao, Chongsheng; Li, Jinkai; Titi, 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.
30. Hong, Min-Chun; Li, Jinkai; Xin, Zhouping Blow-up criteria of strong solutions to the Ericksen-Leslie system in R3. Comm. Partial Differential Equations 39 (2014), no. 7, 1284–1328.
31. Gong, Huajun; Li, Jinkai Global existence of strong solutions to incompressible MHD. Commun. Pure Appl. Anal. 13 (2014), no. 3, 1337–1345.
32. Li, Jinkai Global strong and weak solutions to inhomogeneous nematic liquid crystal flow in two dimensions. Nonlinear Anal. 99 (2014), 80–94.
33. Yin, Jingxue; Li, Jinkai; Ke, Yuanyuan Existence of positive solutions for the p(x)-Laplacian equation. Rocky Mountain J. Math. 42 (2012), no. 5, 1675–1758.
34. Li, Jinkai; Yin, Jingxue; Ke, Yuanyuan Existence of positive solutions for the p-Laplacian with p-gradient term. J. Math. Anal. Appl. 383 (2011), no. 1, 147–158.
35. Yin, Jingxue; Li, Jinkai; Ke, Yuanyuan Existence of solutions for the p-Laplacian with critical Sobolev exponent and convection. Appl. Anal. 89 (2010), no. 10, 1575–1590.