Incompressible limit of the non-isentropic ideal magnetohydrodynamic equations

TL;DR

This paper investigates the behavior of solutions to the compressible non-isentropic ideal magnetohydrodynamic equations as the Mach number approaches zero, demonstrating convergence to incompressible MHD equations with uniform estimates.

Contribution

It establishes the existence of solutions independent of Mach number and proves their convergence to incompressible MHD equations in the zero Mach limit.

Findings

Solutions exist uniformly in Mach number

Solutions converge to incompressible MHD equations

Uniform a priori estimates are derived

Abstract

We study the incompressible limit of the compressible non-isentropic ideal magnetohydrodynamic equations with general initial data in the whole space $\mathbb{R}^d$ ($d=2,3$). We first establish the existence of classic solutions on a time interval independent of the Mach number. Then, by deriving uniform a priori estimates, we obtain the convergence of the solution to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero.