Global existence and incompressible limit of weak solutions to the multi-dimensional compressible magnetohydrodynamics

The equations for the three-dimensional viscous and compressible magnetohydrodynamic (MHD) flows are considered in the isentropic case. First an initial-boundary value problem is studied in a bounded domain with large data. The existence and large-time behavior of global weak solutions are established through a three-level approximation, energy estimates, and weak convergence for certain adiabatic exponents and constant viscosity coefficients. Then the relation between the compressible MHD flows with low Mach number and the incompressible MHD flows, that is, the zero Mach number limit for the weak solutions, is discussed.