Some recent results on compressible Navier-Stokes equations
报告题目(Title)：Some recent results on compressible Navier-Stokes equations
报告人(Speaker)：李竞，研究员，中国科学院应用数学所
地点(Place)：后主楼1220
时间(Time)：5月28日下午2:00-3:00
邀请人(Inviter)：许孝精
报告摘要
In this talk, I 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.)
