教育背景
工作经历
开设课程
科研项目
学术成果
社会兼职
其他




李进开
研究员 华南数学应用与交叉研究中心
研究方向: 偏微分方程
jklimath@m.scnu.edu.cn; jklimath@gmail.com




教育背景
2010/08--2013/07: 香港中文大学 数学研究所 博士
2006/08--2008/07：吉林大学 数学研究所 硕士
2002/08--2006/07：吉林大学 数学学院 本科



工作经历
2018/07--至今 华南师范大学 华南数学应用与交叉研究中心 研究员
2016/08--2018/06 香港中文大学 数学系 研究助理教授
2013/08--2016/07 Weizmann Institute of Sciences 博士后



开设课程
2019--2020学年度：Sobolev空间及L^2理论



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**；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2019A；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**；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**；48万；参与



学术成果
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)
Gong, Huajun; Li, Jinkai; Liu, Xiangao; Zhang, Xiaotao: Local well-posedness of isentropic compressible Navier-Stokes equations with vacuum. Commun. Math. Sci. (2020 accepted)
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)
Li, Jinkai;Global well-posedness of non-heat conductive compressible Navier-Stokes equations in 1D. Nonlinearity 33 (2020), 2181–2210
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.
Bian, Dongfen;Li, JinkaiFinite time blow up of compressible Navier-Stokes equations on half space or outside a fixed ball.J. Differential Equations267(2019),no. 12,7047–7063.
Li, JinkaiGlobal 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.
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.
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.
Li, Jinkai;Xu, Zhonghai;Zhang, JianwenGlobal 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.
Gong, Huajun;Huang, Tao;Li, JinkaiNonuniqueness of nematic liquid crystal flows in dimension three.J. Differential Equations263(2017),no. 12,8630–8648.
Hittmeir, Sabine;Klein, Rupert;Li, Jinkai;Titi, Edriss S.Global well-posedness for passively transported nonlinear moisture dynamics with phase changes.Nonlinearity30(2017),no. 10,3676–3718.
Li, JinkaiLocal existence and uniqueness of strong solutions to the Navier-Stokes equations with nonnegative density.J. Differential Equations263(2017),no. 10,6512–6536.
Cao, Chongsheng;Li, Jinkai;Titi, Edriss S.Strong solutions to the 3D primitive equations with only horizontal dissipation: nearH1initial data.J. Funct. Anal.272(2017),no. 11,4606–4641.
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.
Gong, Huajun;Li, Jinkai;Xu, ChenLocal well-posedness to inhomogeneous Ericksen-Leslie system with general Leslie stress tensor.Z. Angew. Math. Phys.68(2017),no. 1,Art. 17, 23 pp.
Gong, Huajun;Li, Jinkai;Xu, ChenLocal well-posedness of strong solutions to density-dependent liquid crystal system.Nonlinear Anal.147(2016),26–44.
Li, Jinkai;Titi, Edriss S.A tropical atmosphere model with moisture: global well-posedness and relaxation limit.Nonlinearity29(2016),no. 9,2674–2714.
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.
Li, Jinkai;Xin, ZhoupingGlobal 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.
Li, Jinkai;Titi, EdrissGlobal well-posedness of strong solutions to a tropical climate model.Discrete Contin. Dyn. Syst.36(2016),no. 8,4495–4516.
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.
Li, Jinkai;Titi, Edriss S.;Xin, ZhoupingOn the uniqueness of weak solutions to the Ericksen-Leslie liquid crystal model inR2.Math. Models Methods Appl. Sci.26(2016),no. 4,803–822.
Fan, Jishan;Li, JinkaiA logarithmic regularity criterion for the 3D generalized MHD system.Math. Methods Appl. Sci.38(2015),no. 18,5279–5283.
Li, JinkaiGlobal strong solutions to the inhomogeneous incompressible nematic liquid crystal flow.Methods Appl. Anal.22(2015),no. 2,201–220.
Fan, Jishan;Li, JinkaiRegularity criteria for the strong solutions to the Ericksen-Leslie system inR3.J. Math. Anal. Appl.425(2015),no. 2,695–703.
Cao, Chongsheng;Li, Jinkai;Titi, Edriss S.Global well-posedness of strong solutions to the 3D primitive equations with horizontal eddy diffusivity.J. Differential Equations257(2014),no. 11,4108–4132.
Ma, Wenya;Gong, Huajun;Li, JinkaiGlobal strong solutions to incompressible Ericksen-Leslie system inR3.Nonlinear Anal.109(2014),230–235.
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.
Hong, Min-Chun;Li, Jinkai;Xin, ZhoupingBlow-up criteria of strong solutions to the Ericksen-Leslie system inR3.Comm. Partial Differential Equations39(2014),no. 7,1284–1328.
Gong, Huajun;Li, JinkaiGlobal existence of strong solutions to incompressible MHD.Commun. Pure Appl. Anal.13(2014),no. 3,1337–1345.
Li, JinkaiGlobal strong and weak solutions to inhomogeneous nematic liquid crystal flow in two dimensions.Nonlinear Anal.99(2014),80–94.
Yin, Jingxue;Li, Jinkai;Ke, YuanyuanExistence of positive solutions for thep(x)-Laplacian equation.Rocky Mountain J. Math.42(2012),no. 5,1675–1758.
Li, Jinkai;Yin, Jingxue;Ke, YuanyuanExistence of positive solutions for thep-Laplacian withp-gradient term.J. Math. Anal. Appl.383(2011),no. 1,147–158.
Yin, Jingxue;Li, Jinkai;Ke, YuanyuanExistence of solutions for thep-Laplacian with critical Sobolev exponent and convection.Appl. Anal.89(2010),no. 10,1575–1590.



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