Incompressible limit of isentropic magnetohydrodynamic equations with ill-prepared data in bounded domains

Abstract

This paper rigorously justifies the incompressible limit of strong solutions to isentropic compressible magnetohydrodynamic equations with ill-prepared initial data in a three-dimensional bounded domain as the Mach number goes to zero. In both cases of viscous and inviscid magnetic fields, we establish a new energy functional with weight to obtain uniform estimates for strong solutions with respect to the Mach number. Then, we prove the weak convergence of a velocity and the strong convergence of a magnetic field and the divergence-free component of a velocity field, which yields the corresponding incompressible limit.