Incompressible limit of the compressible magnetohydrodynamic equations with vanishing viscosity coefficients

Abstract

This paper is concerned with the incompressible limit of the compressible magnetohydrodynamic equations with vanishing viscosity coefficients and general initial data in the whole space ${\mathbb{R}}^d$ $(d=2$ or 3). 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.

17pages. We have improved our paper according to the referees' suggestions

References in corpus (3)

• Global Existence and Large-Time Behavior of Solutions to the Three-Dimensional Equations of Compressible Magnetohydrodynamic Flows
• Global solutions to the three-dimensional full compressible magnetohydrodynamic flows
• Incompressible limit of the compressible magnetohydrodynamic equations with vanishing viscosity coefficients

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