Low Mach number limit for the full compressible magnetohydrodynamic equations with general initial data

Abstract

The low Mach number limit for the full compressible magnetohydrodynamic equations with general initial data is rigorously justified in the whole space R3. First, the uniform-in-Mach-number estimates of the solutions in a Sobolev space are established on a finite time interval independent of the Mach number. Then the low Mach number limit is proved by combining these uniform estimate with a theorem due to Métivier and Schochet (2001) [45] for the Euler equations that gives the local energy decay of the acoustic wave equations.