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This paper is concerned with the incompressible limit of the compressiblemagnetohydrodynamic equations with vanishing viscosity coefficients and generalinitial data in the whole space $\mathbb{R}^d$ $ (d=2$ or 3). It is rigorouslyshowed that, as the Mach number, the shear viscosity coefficient and themagnetic diffusion coefficient simultaneously go to zero, the weak solution ofthe compressible magnetohydrodynamic equations converges to the strong solutionof the ideal incompressible magnetohydrodynamic equations as long as the latterexists.

Incompressible Limit of the Compressible Magnetohydrodynamic Equations with Vanishing Viscosity Coefficients