Convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations in a bounded domain

TL;DR

This paper proves that solutions of the full compressible Navier-Stokes-Maxwell system converge to the incompressible magnetohydrodynamic equations in a bounded domain as the Mach number and dielectric constant tend to zero, using uniform estimates.

Contribution

It establishes uniform estimates and convergence results for the full compressible Navier-Stokes-Maxwell system to MHD equations in a bounded domain, which was previously unaddressed.

Findings

Uniform estimates of strong solutions with respect to Mach number and dielectric constant.

Convergence of the system to incompressible MHD equations for well-prepared data.

Validation of the asymptotic limit in a bounded domain setting.

Abstract

In this paper we establish the uniform estimates of strong solutions with respect to the Mach number and the dielectric constant to the full compressible Navier-Stokes-Maxwell system in a bounded domain. Based on these uniform estimates, we obtain the convergence of the full compressible Navier-Stokes-Maxwell system to the incompressible magnetohydrodynamic equations for well-prepared data.