Combined Incompressible and Inviscid Limit of the Compressible Magnetohydrodynamic Equations in the Whole Space

Abstract. This paper is concerned with the combined incompressible and inviscid limit of the compressible magnetohydrodynamic equations in the whole space with general initial data. It is rigorously showed that, as the Mach number, the shear viscosity coefficient and the magnetic diffusion coefficient simultaneously go to zero, the weak solution of the compressible magnetohydrodynamic equations converges to the strong solution of the ideal incompressible magnetohydrodynamic equations as long as the latter exists. The proof of the result relies on the new modulated energy functional and the Strichartz’s estimate of linear wave equations.