BLOW-UP OF CLASSICAL SOLUTIONS TO THE COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH VACUUM

doi:10.1016/S0252-9602(15)30090-4

Abstract

Abstract:

In this paper, we consider the formation of singularity for the classical solutions to compressible MHD equations without thermal conductivity or infinity electric conductivity when the initial data contains vacuum. We show that the life span of any smooth solution will not be extended to ∞, if the initial vacuum only appears in some local domain and the magnetic field vanishes on the interface that separates the vacuum and non-vacuum state, regardless the size of the initial data or the far field state.

Key words: MHD, infinity electric conductivity, classical solutions, vacuum, blow-up

CLC Number:

35A09

Shengguo ZHU. BLOW-UP OF CLASSICAL SOLUTIONS TO THE COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH VACUUM[J].Acta mathematica scientia,Series B, 2016, 36(1): 220-232.

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