• Littlewood-Paley 理论及其在不可压Navier-Stokes 方程、Euler 方程、Quasigeostrophic(QG)方程和Magnetohydrodynamics(MHD)方程等流体动力学方程中的应用
• 非线性抛物方程和分数阶耗散方程

   

070101-基础数学

偏微分方程

2006-09--2009-07   中国工程物理研究院   理学博士
2001-09--2003-07   吉林大学   理学硕士
1997-09--2001-07   吉林大学   理学学士

   

2015-11~现在, 中国科学院大学, 副教授
2011-06~2015-11,中国科学院大学, 讲师
2009-07~2011-06,中国科学院数学与系统科学研究院, 博士后
2003-07~2006-07,东北大学东软信息学院, 讲师

微积分II-A
微积分II习题课-A01-1
微积分I习题-A01-1
微积分I-A
微积分Ⅲ习题-A02-1
微积分III
微积分II习题课-A02-1
微积分Ⅲ习题-A01-1
微积分I习题-A02-1
微积分II习题课-A03-1
微积分Ⅱ-A
微积分I习题-A03-1
微积分II习题课-B01-1
微积分Ⅱ-B
微积分II-B
微积分I习题-B01-1
微积分I-B
微积分I习题课-B01-1
微积分Ⅲ-B01-2
微积分III-B
微积分III习题课-B01-1
偏微分方程概论Ⅱ
数学物理方程（电子与通信类）
抛物型偏微分方程

   

（1） Stability of singular solutions to the Navier-Stokes system, JOURNAL OF DIFFERENTIAL EQUATIONS, 2022, 第 4 作者
（2） ON CONTINUATION CRITERIA FOR THE FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS IN LORENTZ SPACES, ON CONTINUATION CRITERIA FOR THE FULL COMPRESSIBLE NAVIER-STOKES EQUATIONS IN LORENTZ SPACES, ACTA MATHEMATICA SCIENTIA, 2022, 第 3 作者
（3） Global well-posedness of strong solution to 2D MHD equations in critical Fourier-Herz spaces, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 第 2 作者
（4） epsilon-Regularity criteria in anisotropic Lebesgue spaces and Leray's self-similar solutions to the 3D Navier-Stokes equations, ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2020, 第 2 作者
（5） A regularity criterion at one scale without pressure for suitable weak solutions to the Navier-Stokes equations, JOURNAL OF DIFFERENTIAL EQUATIONS, 2019, 第 2 作者
（6） Global Mild Solution of Stochastic Generalized Navier-Stokes Equations with Coriolis Force, Global Mild Solution of Stochastic Generalized Navier-Stokes Equations with Coriolis Force, ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2018, 第 2 作者
（7） Global Well-posedness of the 3D Generalized Rotating Magnetohydrodynamics Equations, ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2018, 第 2 作者
（8） 三维广义磁流体方程组解的最优衰减率, Optimal Decay Estimates of Solutions to the Three-dimensional Generalized MHD Equations, 数学学报, 2018, 第 2 作者
（9） Endpoint regularity criterion for weak solutions of the 3D incompressible liquid crystals system, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 第 3 作者
（10） Global mild solution of the generalized Navier–Stokes equations with the Coriolis force, APPLIED MATHEMATICS LETTERS, 2018, 第 2 作者
（11） Some Interior Regularity Criteria Involving Two Components for Weak Solutions to the 3D Navier-Stokes Equations, JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2018, 第 2 作者
（12） Remarks on the singular set of suitable weak solutions for the three-dimensional Navier-Stokes equations, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 第 3 作者
（13） On the box-counting dimension of the potential singular set for suitable weak solutions to the 3D Navier-Stokes equations, NONLINEARITY, 2017, 第 2 作者
（14） Partial regularity of suitable weak solutions to the multi-dimensional generalized magnetohydrodynamics equations, COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2016, 第 3 作者
（15） Refined regularity class of suitable weak solutions to the 3D magnetohydrodynamics equations with an application, ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2016, 第 2 作者
（16） Partial Regularity of the Suitable Weak Solutions to the Multi-dimensional Incompressible Boussinesq Equations, JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2016, 第 3 作者
（17） Anisotropic regularity conditions for the suitable weak solutions to the 3d navier-stokes equations, JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2016, 第 2 作者
（18） Local regularity criteria of the 3D Navier-Stokes and related equations, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 第 2 作者
（19） Partial regularity for the 3d magneto-hydrodynamics system with hyper-dissipation, ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2015, 第 2 作者
（20） A unified proof on the partial regularity for suitable weak solutions of non-stationary and stationary Navier–Stokes equations, JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 第 2 作者
（21） Global well-posedness of the aggregation equation with supercritical dissipation in Besov spaces, ZAMMZEITSCHRIFTFURANGEWANDTEMATHEMATIKUNDMECHANIK, 2013, 第 1 作者
（22） Global well-posedness for the two-dimensional nonlinear Boussinesq equations with vertical dissipation, JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 通讯作者
（23） Global well-posedness for the 2D inviscid Benard system with fractional diffusivity and Yudovich's type data, JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 第 1 作者
（24） Global well-posedness for Navier-Stokes equations in critical Fourier-Herz spaces, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 第 2 作者
（25） On the well-posedness for Keller-Segel system with fractional diffusion, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2011, 通讯作者
（26） A remark on the Lipschitz estimates of solutions to Navier-Stokes equations, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2010, 通讯作者
（27） Inviscid limit for axisymmetric flows without swirl in a critical Besov space, ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2010, 通讯作者
（28） Local well-posedness of the viscous rotating shallow water equations with a term of capillarity, ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2010, 通讯作者
（29） Regularity criteria for the 3D generalized MHD equations in terms of vorticity, NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 通讯作者
（30） Global well-posedness of the critical Burgers equation in critical Besov spaces, JOURNAL OF DIFFERENTIAL EQUATIONS, 2009, 第 2 作者
（31） Two-dimensional chemotaxis models with fractional diffusion, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2009, 第 2 作者
（32） Well-posedness of the Cauchy problem for the fractional power dissipative equation in critical Besov spaces, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 通讯作者
（33） On the inviscid limit of the two-dimensional Navier-Stokes equations with fractional diffusion, 2008, 第 1 作者
（34） Local well-posedness of the Cauchy problem for the generalized Camassa-Holm equation in Besov spaces, 2007, 第 1 作者
（35） 以Dirac测度为源的拟线性退化抛物方程, QUASILINEAR DEGENERATE PARABOLIC EQUATION WITH DIRAC MEASURE, 数学年刊A辑, 2005, 第 2 作者
（36） Remarks on the singular set of suitable weak solutions to the 3D Navier-Stokes equations, JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 第 3 作者

   

（ 1 ） 流体动力学方程的调和分析方法, 负责人, 国家任务, 2012-01--2014-12
（ 2 ） 几类非线性发展方程的数学理论, 参与, 其他国际合作项目, 2012-05--2014-04
（ 3 ） 微分算子特征值的最优估计, 参与, 国家任务, 2017-01--2020-12
（ 4 ） 关于一些流体动力学方程的数学理论, 负责人, 国家任务, 2018-01--2021-12

现指导学生

敏德载  硕士研究生  070101-基础数学  

姚卓雅  硕士研究生  070101-基础数学