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题目： Some recent results on compressible Navier-Stokes equations

报告人：李竞 研究员 （中科院&南昌大学）

时间：2021年11月15日下午 2：30-3：30

地点：腾讯会议  会议ID：679 487 135

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 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.)

联系人： 牛冬娟

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