Acta mathematica scientia, Series B >
BLOW-UP OF CLASSICAL SOLUTIONS TO THE COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH VACUUM
Received date: 2014-09-29
Revised date: 2015-01-11
Online published: 2016-01-30
Supported by
The research was supported in part by National Natural Science Foundation of China(11231006), Natural Science Foundation of Shanghai(14ZR1423100) and China Scholarship Council.
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
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 . DOI: 10.1016/S0252-9602(15)30090-4
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