Local well-posedness and low Mach number limit of the compressible magnetohydrodynamic equations in critical spaces

Fucai Li; Yanmin Mu; Dehua Wang

doi:10.3934/krm.2017030

Article Contents

2017, Volume 10, Issue 3: 741-784. Doi: 10.3934/krm.2017030

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Local well-posedness and low Mach number limit of the compressible magnetohydrodynamic equations in critical spaces

1.
Department of Mathematics, Nanjing University, Nanjing 210093, China
2.
School of Applied Mathematics, Nanjing University of Finance & Economics, Nanjing 210046, China
3.
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA

Y. Mu is the corresponding author
Y. Mu is the corresponding author

Received: July 2016

Revised: October 2016

Published: September 2017

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Abstract

The local well-posedness and low Mach number limit are considered for the multi-dimensional isentropic compressible viscous magnetohydrodynamic equations in critical spaces. First the local well-posedness of solution to the viscous magnetohydrodynamic equations with large initial data is established. Then the low Mach number limit is studied for general large data and it is proved that the solution of the compressible magnetohydrodynamic equations converges to that of the incompressible magnetohydrodynamic equations as the Mach number tends to zero. Moreover, the convergence rates are obtained.

Keywords:

Isentropic compressible magnetohydrodynamic equations,
incompressible magnetohydrodynamic equations,
local well-posedness,
low Mach number limit,
critical spaces.

Mathematics Subject Classification: Primary: 76W05; Secondary: 35B40.

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References

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