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2021 年《变分法小型讨论会》（十八）

Miniworkshop on Variational Methods-18  

报告人：李竞  研究员

             南昌大学 & 中科院数学与系统科学研究院

报告题目：Some recent results on compressible Navier-Stokes equations  

Abstract: We investigate the barotropic compressible Navier-Stokes equations with slip boundary conditions in a three-dimensional (3D) simply connected bounded domain, whose smooth boundary has a finite number of two-dimensional connected components. For any adiabatic exponent bigger than one, after obtaining some new estimates on boundary integrals related to the  slip boundary condition, we prove that both the weak and classical solutions to the initial-boundary-value problem of this system exist globally in time provided the initial energy is suitably small. Moreover, the density has large oscillations and contains vacuum states. Finally, it is also shown that for the classical solutions, the oscillation of the density will grow unboundedly in the long run with an exponential rate provided vacuum appears (even at a point) initially. This is the first result concerning the global existence of classical solutions to the compressible Navier-Stokes equations with density containing vacuum states initially for general 3D bounded smooth domains. This is a joint work with Prof. Guocai Cai (Xiamen Univ.)

报告人简介：  

李竞研究员, 南昌大学 & 中科院数学与系统科学研究院，国家杰出青年基金获得者，主要研究方向为可压缩 Navier-Stokes 方程，李竞研究员证明了三维空间可压缩 Navier-Stokes方程含真空的大震荡古典解的整体存在性等一系列结果，其研究工作发表在国际著名数学杂志“Comm. Pure Appl. Math.”、“Arch. Ration. Mech. Anal.”“Comm. Math.Phys.”、“J. Math. Pures Appl. ”和“SIAM J. Math. Anal.”。  

时间：2021 年 6 月 24 日，10:00-11:00

腾讯会议: 873 353 100，会议密码：0624  

联系人：苏加宝，田如顺

欢迎各位老师同学参加！