In this talk, we are concerned with the propagation of the regularity for the non-isentropic Navier-Stokes system in a domain with boundaries, uniformly in the Mach number and the Reynolds number, in a general setting of ill-prepared data. This is an essential step towards the study of the low Mach number and the inviscid limit for strong solutions. The main obstacle to estabilish such uniform regularity estimates lie in the existence of fast oscillating acoustic waves (due to the ill-prepared assumption) and the interactions of two kinds of boundary layers (due to the large time temperature variation and the non-vanishing thermal conductivity). To start, I will first explain the ideas to propagate the high regularity for the isentropic Navier-Stokes system uniformly only in Mach number, which was a joint work with Professor N. Masmoudi and F. Rousset.
This video was produced by the SITE Research Center at New York University, as part of their talk series.
