数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (6): 1851-1864.doi: 10.1016/S0252-9602(10)60178-6

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A BLOW-UP CRITERION FOR COMPRESSIBLE VISCOUS HEAT-CONDUCTIVE FLOWS

江松|欧耀彬   

  1. LCP, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, China
  • 收稿日期:2010-03-08 出版日期:2010-11-20 发布日期:2010-11-20
  • 基金资助:

    The research of Ou is partially supported by the China Postdoctoral Science Foundation (20090450333). Jiang is supported by the National Basic Research Program (2005CB321700) and NSFC (40890154).

A BLOW-UP CRITERION FOR COMPRESSIBLE VISCOUS HEAT-CONDUCTIVE FLOWS

 JIANG Song, OU Yao-Bin   

  1. LCP, Institute of Applied Physics and Computational Mathematics, P. O. Box 8009, Beijing 100088, China
  • Received:2010-03-08 Online:2010-11-20 Published:2010-11-20
  • Supported by:

    The research of Ou is partially supported by the China Postdoctoral Science Foundation (20090450333). Jiang is supported by the National Basic Research Program (2005CB321700) and NSFC (40890154).

摘要:

We study an initial boundary value problem for the Navier-Stokes equations of compressible viscous heat-conductive fluids in a 2-D periodic domain or the unit square domain. We establish a blow-up criterion for the local strong solutions in terms of the gradient of the velocity only, which coincides with the famous Beale-Kato-Majda criterion for ideal incompressible flows.

关键词: blow-up criteria, strong solutions, compressible Navier-Stokes equations, heat-conductive flows

Abstract:

We study an initial boundary value problem for the Navier-Stokes equations of compressible viscous heat-conductive fluids in a 2-D periodic domain or the unit square domain. We establish a blow-up criterion for the local strong solutions in terms of the gradient of the velocity only, which coincides with the famous Beale-Kato-Majda criterion for ideal incompressible flows.

Key words: blow-up criteria, strong solutions, compressible Navier-Stokes equations, heat-conductive flows

中图分类号: 

  • 76N10