Low Mach number limit of Navier-Stokes equations with large temperature variations in bounded domains

Abstract

The low Mach number limit of full compressible Navier-Stokes equations with large temperature variations is verified rigorously in a three-dimensional bounded domain. Weighted uniform estimates of the solutions are derived in a time interval which is independent of the Mach number, in particular, for the high-order derivatives, when the initial data are well-prepared only in the sense of L2-norm. It can be viewed as the first result on the low Mach number limit of full Navier-Stokes equations with large temperature variations in bounded domains. The methods in the paper also apply to other fluid models with large temperature variations.