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The low Mach number limit for the full compressible magnetohydrodynamic equations with general initial data is rigorously justified in the whole space R³. The uniform in Mach number estimates of the solutions in a Sobolev space are obtained on a time interval independent of the Mach number. The limit is proved by using the established uniform estimates and a theorem due to Métiver and Schochet Arch. Ration. Mech. Anal. 158 (2001), 61-90 for the Euler equations that gives the local energy decay of the acoustic wave equations.
Jiang et al. (Sat,) studied this question.