非线性偏微分方程，可压缩Navier-Stokes方程

   

070101-基础数学

偏微分方程
可压缩Navier-Stokes方程

   

现代偏微分方程I、II

   

（1） 世界华人数学家联盟五年最佳论文, 二等奖, 其他, 2020
（2） 首届世界华人数学家联盟年会（ICCM）“五年最佳银奖论文”, 二等奖, 其他, 2017

   

（1） Local weak solution of the isentropic compressible Navier-Stokes equations with variable viscosity, Journal of Mathematical Fluid Mechanics, 2024, 第 2 作者
（2） Global large strong solutions to the radially symmetric compressible Navier-Stokes equations in 2D solid balls, Journal of Differential Equations, 2024, 第 1 作者
（3） Global well-posedness of classical solutions to the cauchy problem of two-dimensional barotropic compressible Navier-Stokes system with vacuum and large initial data, SIAM J. MATH. ANAL., 2022, 第 1 作者
（4） Local weak solutions of the isentropic compressible Navier-Stokes equations in a half-space, Science. China Math, 2022, 第 1 作者
（5） On local strong and classical solutions to the three-dimensional barotropic compressible Navier-Stokes equations with vacuum, SCIENCE CHINA-MATHEMATICS, 2021, 通讯作者
（6） Local weak solutions of the isentropic compressible Navier-Stokes equations, J. Math. Phys, 2021, 通讯作者
（7） On center singularity for compressible spherically symmetric nematic liquid crystal flows, JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 第 2 作者
（8） Global well-posedness of classical solutions to the three-dimensional full compressible Navier-Stokes system with vacuum, Arch. Ration. Mech. Anal., 2018, 第 1 作者
（9） A representation formula of incompressible liquid crystal flow and its applications, NONLINEARITY, 2017, 通讯作者
（10） Existence and uniqueness of weak solutions of the compressible spherically symmetric Navier–Stokes equations, JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 第 1 作者
（11） Linfinity continuation principle to the non-barotropic non-resistive magneto-hydrodynamic equations without heat conductivity., Mathematical Methods in the Applied Sciences, 2016, 第 1 作者
（12） Existence and blowup behavior of global strong solutions to the two-dimensional barotropic compressible Navier-Stokes system with vacuum and large initial data, J. Math. Pures Appl., 2016, 第 1 作者
（13） ON FORMATION OF SINGULARITY FOR NON-ISENTROPIC NAVIER-STOKES EQUATIONS WITHOUT HEAT-CONDUCTIVITY, DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 第 1 作者
（14） On formation of singularity of spherically symmetric nonbarotropic flows, KYOTO JOURNAL OF MATHEMATICS, 2015, 通讯作者
（15） A CHARACTERIZATION ON BREAKDOWN OF SMOOTH SPHERICALLY SYMMETRIC SOLUTIONS OF THE ISENTROPIC SYSTEM OF COMPRESSIBLE NAVIER-STOKES EQUATIONS, OSAKA JOURNAL OF MATHEMATICS, 2015, 通讯作者
（16） Global strong solution of 3D inhomogeneous Navier-Stokes equations with density-dependent viscosity, JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 第 1 作者
（17） GLOBAL STRONG SOLUTION WITH VACUUM TO THE TWO DIMENSIONAL DENSITY-DEPENDENT NAVIER-STOKES SYSTEM, SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2014, 通讯作者
（18） On some new global existence results for 3D magnetohydrodynamic equations, NONLINEARITY, 2014, 第 2 作者
（19） Serrin-Type Blowup Criterion for Viscous, Compressible, and Heat Conducting Navier-Stokes and Magnetohydrodynamic Flows, COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2013, 通讯作者
（20） Serrin-Type Blowup Criterion for Full Compressible Navier-Stokes System, ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2013, 通讯作者
（21） Global strong solution to the 2D nonhomogeneous incompressible MHD system, JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 第 1 作者
（22） Global Wellposedness for the 3D Inhomogeneous Incompressible Navier-Stokes Equations, JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2013, 第 2 作者
（23） A Serrin criterion for compressible nematic liquid crystal flows, MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2013, 第 1 作者
（24） Global Weak Solutions to One-Dimensional Non-Conservative Viscous Compressible Two-Phase System, COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2012, 第 2 作者
（25） Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations, COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2012, 通讯作者
（26） Blowup Criterion for Viscous Baratropic Flows with Vacuum States, COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2011, 通讯作者
（27） A Multi-Fluid Compressible System as the Limit of Weak Solutions of the Isentropic Compressible Navier-Stokes Equations, ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2011, 
（28） SERRIN-TYPE CRITERION FOR THE THREE-DIMENSIONAL VISCOUS COMPRESSIBLE FLOWS, SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2011, 通讯作者
（29） A blow-up criterion for classical solutions to the compressible Navier-Stokes equations, SCIENCE CHINA-MATHEMATICS, 2010, 第 1 作者
（30） On breakdown of solutions to the full compressible Navier-Stokes equations, Methods and applications of analysis, 2009, 第 1 作者
（31） A blowup criterion for the full compressible Navier-Stokes equations, Methods and applications of analysis, 2009, 第 1 作者

   

（ 1 ） 流体力学方程中的大震荡和低正则解, 负责人, 国家任务, 2020-01--2023-12
（ 2 ） 高维激波以及非线性守恒律方程的低正则解, 参与, 国家任务, 2018-01--2022-12
（ 3 ） Navier-Stokes方程组的若干存在性问题, 负责人, 国家任务, 2015-01--2018-12
（ 4 ） 可压缩流体方程组的若干数学理论研究, 参与, 国家任务, 2017-01--2020-12
（ 5 ） 流体力学方程组的数学理论, 参与, 国家任务, 2021-11--2026-11
（ 6 ） Navier-Stokes方程的解, 负责人, 中国科学院计划, 2022-07--2027-07

（1）On existence and blowup behavior of the compressible Navier-Stokes equations and related models: from Nash’s conjecture to front edge   世界华人数学家大会   2022-07-31
（2）Global classical and weak solutions to the three-dimenional full compressible Navier-Stokes system with vacuum and large oscillations   第四届世界华人数学家联盟年会   2020-12-27
（3）Global large solutions of two dimensional compressible Navier–Stokes equations in the whole space   流体力学数学理论国际研讨会   2019-07-04
（4）Global large solutions of two dimensional compressible Navier–Stokes equations in the whole space   2019-06-04
（5）Global large solutions of two dimensional compressible Navier–Stokes equations in the whole space   2019京川偏微分方程学术会议   2019-04-30
（6）Global solvability of full compressible Naiver-Stokes equations   中国工业与应用数学学会第十六届年会   2018-09-13
（7）Global large solutions of two dimensional compressible Navier–Stokes equations in the whole space   流体力学中的偏微分方程国际学术会议   2018-05-25
（8）Global well-posedness of classical solutions with large oscillations and vacuum to the three dimensional isentropic compressible Navier-Stokes equations   2018-03-14
（9）Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations   第一届世界华人数学家联盟年会   2017-12-27