报告题目：Uniform regularity in the low Mach number and the inviscid limits for the non-isentropic Navier-Stokes system
In fluid mechanics, an important physical quantity that measures the compressibility of a fluid is the so called Mach number. When it is very small, the compressible fluids tend to behave like the incompressible ones. This approximation process is referred to the low Mach numebr limit. We are interested in the justification of this limit process for the strong solutions to the compresible Navier-Stokes system in a domain with boundaries.
The crucial step towards this goal is to establish high regularity estimates uniformly in the Mach number, so that the solutions exist on a time interval independent of the Mach number.
In the first talk, we will focus on the propagation of the uniform regularity for the isentropic Navier-Stokes system in a domain either with fixed boundaries or with free boundaries. The appreance of the boundary layer with fast time oscillations are the main obstacle. These are joint works with Professors N. Masmoudi (NYU, Abu Dhabi) and F. Rousset (Orsay, France).
In the second talk, we study the more general non-isentopic viscous system and aim to prove the uniform estimates not only in the Mach number but also in the Reynolds number (another important physical quantity characterizing the viscosity of a fluid), which enables one to consider simultaneously the low mach number and the inviscid limits for strong solutions.
Compared to the isentropic system with estimates uniform only in the Mach number, some new difficulties arise due to the non-constant temperature and the interactions of two kinds of boundary layers.