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

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

数学物理学报(英文版) ›› 2016, Vol. 36 ›› Issue (1): 220-232.doi: 10.1016/S0252-9602(15)30090-4

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

朱圣国^1,2

1. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China;
2. School of Mathematics, Georgia Tech Atlanta 30332, USA

收稿日期:2014-09-29 修回日期:2015-01-11 出版日期:2016-01-30 发布日期:2016-01-30
作者简介:Shengguo ZHU,E-mail:zhushengguo@sjtu.edu.cn
基金资助:
The research was supported in part by National Natural Science Foundation of China(11231006), Natural Science Foundation of Shanghai(14ZR1423100) and China Scholarship Council.

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

Shengguo ZHU^1,2

1. Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China;
2. School of Mathematics, Georgia Tech Atlanta 30332, USA

Received:2014-09-29 Revised:2015-01-11 Online:2016-01-30 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.

摘要/Abstract

摘要：

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.

关键词: MHD, infinity electric conductivity, classical solutions, vacuum, blow-up

Abstract:

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

中图分类号:

35A09

朱圣国. BLOW-UP OF CLASSICAL SOLUTIONS TO THE COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH VACUUM[J]. 数学物理学报(英文版), 2016, 36(1): 220-232.

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

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

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