Global Classical Solutions to 3D Compressible Magnetohydrodynamic Equations with Large Oscillations and Vacuum

We consider the Cauchy problem of three-dimensional isentropic compressible magnetohydrodynamic equations in the present paper. For regular initial data with small energy but possibly large oscillations, we prove the global well-posedness of classical solution, where the flow density is allowed to c...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis 2013-01, Vol.45 (3), p.1356-1387
Main Authors: Li, Hai-Liang, Xu, Xinying, Zhang, Jianwen
Format: Article
Language:English
Subjects:
Applied mathematics
Cauchy problem
Cauchy problems
Density
Energy of solution
Fourier transforms
Magnetohydrodynamic equations
Mathematical analysis
Navier-Stokes equations
Oscillations
Three dimensional
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Summary:We consider the Cauchy problem of three-dimensional isentropic compressible magnetohydrodynamic equations in the present paper. For regular initial data with small energy but possibly large oscillations, we prove the global well-posedness of classical solution, where the flow density is allowed to contain vacuum states, and the large-time behavior of the solution is also shown. [PUBLICATION ABSTRACT]
ISSN:0036-1410
1095-7154
DOI:10.1137/120893355