Asymptotic limits of the isentropic compressible viscous magnetohydrodynamic equations with Navier-slip boundary conditions

In this paper, two kinds of asymptotic limits to the isentropic compressible viscous magnetohydrodynamic equations in a three-dimensional bounded domain Ω with Navier-slip boundary conditions are discussed. One is the incompressible limit with ill-prepared initial data, and the other is the combined inviscid and incompressible limit with well-prepared initial data. In the first case, we show that the weak solutions of the compressible viscous …