数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (5): 1883-1900.doi: 10.1016/S0252-9602(12)60147-7

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A BLOW-UP CRITERION FOR 3-D NON-RESISTIVE COMPRESSIBLE HEAT-CONDUCTIVE MAGNETOHYDRODYNAMIC EQUATIONS#br# WITH INITIAL VACUUM

徐新英   

  1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • 收稿日期:2011-02-24 修回日期:2011-10-26 出版日期:2012-09-20 发布日期:2012-09-20
  • 基金资助:

    This work was supported by NSFC (11171228, 10801111, 10971171), the fundamental Research Funds for the Central University (2010121006) and the Natural Science Foundation of Fujian Province of China (2010J05011).

A BLOW-UP CRITERION FOR 3-D NON-RESISTIVE COMPRESSIBLE HEAT-CONDUCTIVE MAGNETOHYDRODYNAMIC EQUATIONS#br# WITH INITIAL VACUUM

 XU Xin-Ying   

  1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China;School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • Received:2011-02-24 Revised:2011-10-26 Online:2012-09-20 Published:2012-09-20
  • Supported by:

    This work was supported by NSFC (11171228, 10801111, 10971171), the fundamental Research Funds for the Central University (2010121006) and the Natural Science Foundation of Fujian Province of China (2010J05011).

摘要:

In this paper, we prove a blow-up criterion of strong solutions to the 3-D vis-cous and non-resistive magnetohydrodynamic equations for compressible heat-conducting flows with initial vacuum. This blow-up criterion depends only on the gradient of velocity and the temperature, which is similar to the one for compressible Navier-Stokes equations.

关键词: compressible magnetohydrodynamics, blow-up criterion, vacuum, zero resis-tivity, heat-conducting flows

Abstract:

In this paper, we prove a blow-up criterion of strong solutions to the 3-D vis-cous and non-resistive magnetohydrodynamic equations for compressible heat-conducting flows with initial vacuum. This blow-up criterion depends only on the gradient of velocity and the temperature, which is similar to the one for compressible Navier-Stokes equations.

Key words: compressible magnetohydrodynamics, blow-up criterion, vacuum, zero resis-tivity, heat-conducting flows

中图分类号: 

  • 76W05