Low Mach Number Limit of Viscous Compressible Magnetohydrodynamic Flows

TL;DR

This paper proves that solutions of compressible viscous magnetohydrodynamic equations converge to incompressible solutions as the Mach number approaches zero, justifying the low Mach number limit in various spatial domains.

Contribution

It establishes the rigorous convergence of weak solutions from compressible to incompressible MHD flows in the low Mach number limit across different domain types.

Findings

Weak solutions of compressible MHD converge to incompressible solutions as Mach number tends to zero.

The convergence is valid in periodic, whole space, and bounded domains.

The low Mach number limit is mathematically justified for viscous compressible MHD flows.

Abstract

The relationship between the compressible magnetohydrodynamic flows with low Mach number and the incompressible magnetohydrodynamic flows is investigated. More precisely, the convergence of weak solutions of the compressible isentropic viscous magnetohydrodynamic equations to the weak solutions of the incompressible viscous magnetohydrodynamic equations is proved as the density becomes constant and the Mach number goes to zero, that is, the corresponding incompressible limits are justified when the spatial domain is a periodic domain, the whole space, or a bounded domain.