Jinkai Li

School of Mathematical Sciences

Field:
     jklimath@m.scnu.edu.cn; jklimath@gmail.com

Aug 2010 – Jul 2013:          PhD, The Chinese University of Hong Kong
Aug 2006 – Jul 2008:          Master of Science, Jilin University
Aug 2002 – Jul 2006:          Bachelor of Science, Jilin University

• July 2018 – present: Professor, South China Research Center for Applied Mathematics and Interdisciplinary Studies (CAMIS), South China Normal University
• Aug 2016 – July 2018: Research Assistant Professor, Department of Mathematics, The Chinese University of Hong Kong
• Aug 3013 – July 2016: Postdoctoral Fellow, Department of Computer Science and Applied Mathematics, Weizmann Institute of Science (Mentor: Prof. Edriss S. Titi) 

2020.01-2023.12: National Natural Science Foundation of China (NNSFC) 11971009, Principle Investigator 
2019.01-2022.12: National Natural Science Foundation of China (NNSFC) 11871005, co-Investigator 
2018.01-2021.12: National Natural Science Foundation of China (NNSFC) 11771156, co-Investigator 
2017.09-2020.08: General Research Fund of Hong Kong Research Grants Council, CUHK-14302917, co-Investigator   

 

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)
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.