The incompressible limit for compressible MHD equations in Lp type critical spaces

In this paper, the global well-posedness and the low Mach number limit for compressible viscous magnetohydrodynamic equations in the critical  Lp-type Besov space are considered. More precisely, we will show that, in the isentropic case, the solution of compressible magnetohydrodynamic equations will converge to that of incompressible magnetohydrodynamic equations when the Mach number tends to zero in the critical Lp framework. Moreover, the convergence rate will be obtained.