Low Mach number limit for the multi-dimensional Full magnetohydrodynamic equations

TL;DR

This paper rigorously justifies the low Mach number limit for multi-dimensional full magnetohydrodynamic equations, including effects of thermal conduction and small entropy variations, establishing convergence to incompressible MHD solutions.

Contribution

It provides the first rigorous analysis of the low Mach number limit for full MHD equations with thermal conduction and small entropy variations, including convergence rates.

Findings

Convergence of compressible to incompressible MHD solutions for small Mach number.

Existence of smooth solutions in the low Mach number regime.

Quantitative convergence rates are established.

Abstract

The low Mach number limit for the multi-dimensional full magnetohydrodynamic equations, in which the effect of thermal conduction is taken into account, is rigorously justified in the framework of classical solutions with small density and temperature variations. Moreover, we show that for sufficiently small Mach number, the compressible magnetohydrodynamic equations admit a smooth solution on the time interval where the smooth solution of the incompressible magnetohydrodynamic equations exists. In addition, the low Mach number limit for the ideal magnetohydrodynamic equations with small entropy variation is also investigated. The convergence rates are obtained in both cases.