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The local well-posedness and low Mach number limit are considered for themulti-dimensional isentropic compressible viscous magnetohydrodynamic equationsin critical spaces. First the local well-posedness of solution to the viscousmagnetohydrodynamic equations with large initial data is established. Then thelow Mach number limit is studied for general large data and it is proved thatthe solution of the compressible magnetohydrodynamic equations converges tothat of the incompressible magnetohydrodynamic equations as the Mach numbertends to zero. Moreover, the convergence rates are obtained.Comment: 37page

Local well-posedness and low Mach number limit of the compressible magnetohydrodynamic equations in critical spaces