Low Mach number limit for the multi-dimensional full magnetohydrodynamic equations

The low Mach number limit for the multi-dimensional full magnetohydrodynamic (MHD) equations, in which the effect of thermal conduction is taken into account, is rigorously justified within the framework of classical solutions with small density and temperature variations. Moreover, we show that for a sufficiently small Mach number, the compressible MHD equations admit a smooth solution on the time interval where the smooth solution of the incompressible MHD equations exists. In addition, the low Mach number limit for the ideal MHD equations with small entropy variation is also investigated. The convergence rates are obtained in both cases.