Incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions

TL;DR

This paper rigorously analyzes the convergence of solutions from compressible to incompressible magnetohydrodynamic equations under periodic boundary conditions, providing convergence rates for well-prepared initial data.

Contribution

It establishes the incompressible limit for both viscous and inviscid cases, including convergence rates for well-prepared initial data.

Findings

Weak solutions converge to strong solutions under certain conditions

Convergence rates are obtained for well-prepared initial data

Results apply to both viscous and inviscid incompressible MHD equations

Abstract

This paper is concerned with the incompressible limit of the compressible magnetohydrodynamic equations with periodic boundary conditions. It is rigorously shown that the weak solutions of the compressible magnetohydrodynamic equations converge to the strong solution of the viscous or inviscid incompressible magnetohydrodynamic equations as long as the latter exists both for the well-prepared initial data and general initial data. Furthermore, the convergence rates are also obtained in the case of the well-prepared initial data.