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

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，国家杰出青年基金获得者)

报告时间：2022年5月27日  15:30-16:30

报告地点：腾讯会议  ID：133-602-907

校内联系人：刘生全

 

报告摘要：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 conditions, 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 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.他和合作者证明了高维空间可压缩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.”、“Ann PDE”“J. Math. Pures Appl. ” 和“ SIAM J. Math. Anal.”。

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