Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (4): 1030-1048.doi: 10.1016/S0252-9602(16)30056-X

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BLOWUP CRITERION FOR THE COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL IN 3D WITH VACUUM

Shijin DING1, Bingyuan HUANG2, Youbo LU1   

  1. 1 School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China;
    2 College of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, China
  • Received:2015-06-28 Revised:2016-01-25 Online:2016-08-25 Published:2016-08-25
  • Contact: Shijin DING,E-mail:dingsj@scnu.edu.cn E-mail:dingsj@scnu.edu.cn
  • Supported by:

    This work is supported by the National Basic Research Program of China (973 Program) (2011CB808002), the National Natural Science Foundation of China (11371152, 11128102, 11071086, and 11571117), the Natural Science Foundation of Guangdong Province (S2012010010408), the Foundation for Distinguished Young Talents in Higher Education of Guangdong (2015KQNCX095), the Major Foundation of Hanshan Normal University (LZ201403), and the Scientific Research Foundation of Graduate School of South China Normal University (2014ssxm04).

Abstract:

In this article, we consider the blowup criterion for the local strong solution to the compressible fluid-particle interaction model in dimension three with vacuum. We establish a BKM type criterion for possible breakdown of such solutions at critical time in terms of both the L(0,T;L6)-norm of the density of particles and the L1(0,T;L)-norm of the deformation tensor of velocity gradient.

Key words: Blowup criterion, compressible fluid-particle interaction model, vacuum

CLC Number: 

  • 35Q30
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