Low Mach number limit of the full Navier-Stokes equations with no-slip boundary conditions and large temperature variations

Abstract

In this paper, we rigorously justify the low Mach number limit of the full compressible Navier-Stokes equations in a three-dimensional smooth bounded domain, subject to the no-slip boundary condition for the velocity and well-prepared initial data. In the presence of heat conduction and large temperature variations, we establish the uniform estimates for strong solutions on a time interval independent of the Mach number by constructing an energy functional in a Sobolev framework. The no-slip boundary condition cannot provide the vorticity boundary relation used in the slip-boundary setting. To overcome this difficulty, a divergence-free Stokes lifting of the boundary trace for the time derivative of the modified velocity is employed to define a test function vanishing on the boundary, which enables the transfer of a priori estimates from the velocity to the temperature.

arXiv comment54 pages, no figures