Low Mach number limit for the multi-dimensional Full magnetohydrodynamic equations

Abstract

The low Mach number limit for the multi-dimensional full magnetohydrodynamic equations, in which the effect of thermal conduction is taken into account, is rigorously justified in the framework of classical solutions with small density and temperature variations. Moreover, we show that for sufficiently small Mach number, the compressible magnetohydrodynamic equations admit a smooth solution on the time interval where the smooth solution of the incompressible magnetohydrodynamic equations exists. In addition, the low Mach number limit for the ideal magnetohydrodynamic equations with small entropy variation is also investigated. The convergence rates are obtained in both cases.

19 pages. We revised our paper by following the referee's comments

References in corpus (2)

• Global solutions to the three-dimensional full compressible magnetohydrodynamic flows
• Incompressible limit of the compressible magnetohydrodynamic equations with vanishing viscosity coefficients

Cited by in corpus (5)

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• Convergence of the complete electromagnetic fluid system to the full compressible magnetohydrodynamic equations
• High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers
• Entropy-bounded solutions to the 3D compressible heat-conducting magnetohydrodynamic equations with vacuum at infinity