Speaker：Yaobin Ou（Renmin University of China）

Time：2022-07-13, 15:00

Location：Tencent Meeting ID：592-310-704（No Password）

Abstract:

In this talk, I first discuss the incompressible limit of strong solutions to the isentropic compressible Navier-Stokes equations with ill-prepared initial data and slip boundary condition in a three-dimensional bounded domain, which is a joint work with Lu Yang. Previous results only deal with the cases of the weak solutions or the cases without solid boundary, where the uniform estimates are much easier to be shown. We propose a new weighted energy functional to establish the uniform estimates, in particular for the time derivatives and the high-order spatial derivatives. The estimates of highest order spatial derivatives of fast variables are crucial for the uniform bounds of solutions. The incompressible limit is shown by applying the Helmholtz decomposition, the weak convergence of the velocity and the strong convergence of its divergence-free component. Next, I discuss related results on the low Mach number limit of non-isentropic Navier-Stokes equations, in particular for the case of well-prepared initial data and/or Dirichlet boundary condition.