LOW MACH NUMBER LIMIT FOR THE COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS IN A PERIODIC DOMAIN

This paper studies the convergence of the compressible isentropic magnetohydrodynamic equations to the corresponding incompressible magnetohydrodynamic equations with ill-prepared initial data in a periodic domain. We prove that the solution to the compressible isentropic magnetohydrodynamic equations with small Mach number exists uniformly in the time interval as long as that to the incompressible one does. Furthermore, we obtain the convergence result for the solutions filtered by the group of acoustics.