Low Mach number limit of full compressible Navier-Stokes equations with revised Maxwell law

TL;DR

This paper investigates the behavior of solutions to the full compressible Navier-Stokes equations with revised Maxwell law as the Mach number approaches zero, establishing convergence to incompressible flow with specific rates.

Contribution

It provides a rigorous proof of the low Mach number limit for these equations, including convergence rates, under the revised Maxwell law framework.

Findings

Solutions converge to incompressible Navier-Stokes solutions as Mach number tends to zero.

Established convergence rates for the low Mach number limit.

Uniform error estimates for the approximation.

Abstract

In this paper, we study the low Mach number limit of the full compressible Navier-Stokes equations with revised Maxwell law. By applying the uniform estimation of the error system, we prove that the solutions of the full compressible Navier-Stokes equations with time relaxation converge to that of the incompressible Navier-Stokes equations as the Mach number tends to zero. Moreover, the convergence rates are also obtained.