数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (4): 1072-1080.doi: 10.1016/S0252-9602(14)60070-9

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LPS´S CRITERION FOR INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS

陈卿|谭忠|吴国春*   

  1. Department of Mathematics and Physics, Xiamen University of Technology, Xiamen 361024, China; School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • 收稿日期:2013-05-24 出版日期:2014-07-20 发布日期:2014-07-20
  • 通讯作者: 吴国春,guochunwu@126.com E-mail:chenqing@xmut.edu.cn;ztan85@163.com;guochunwu@126.com
  • 基金资助:

    The research was supported Supported by National Natural Science Foundation of China (10976026, 11271305, 11301439, 11226174).

LPS´S CRITERION FOR INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS

 CHEN Qing, TAN Zhong, WU Guo-Chun*   

  1. Department of Mathematics and Physics, Xiamen University of Technology, Xiamen 361024, China; School of Mathematical Sciences, Xiamen University, Xiamen 361005, China  
  • Received:2013-05-24 Online:2014-07-20 Published:2014-07-20
  • Contact: WU Guo-Chun,guochunwu@126.com E-mail:chenqing@xmut.edu.cn;ztan85@163.com;guochunwu@126.com
  • Supported by:

    The research was supported Supported by National Natural Science Foundation of China (10976026, 11271305, 11301439, 11226174).

摘要:

In this paper we derive LPS´s criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in R3. We show that if 0 < T < +∞ is the maximal time interval for the unique smooth solution u C([0, T),R3),
then |u| + |∇d| /∈ Lq([0, T], Lp(R3)), where p and q safisfy the Ladyzhenskaya-Prodi-Serrin´s condition: 3/p+2/q= 1 and p ∈ (3,+∞].

关键词: incompressible nematic liquid crystal flow, Ladyzhenskaya-Prodi-Serrin´s cri-terion

Abstract:

In this paper we derive LPS´s criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in R3. We show that if 0 < T < +∞ is the maximal time interval for the unique smooth solution u C([0, T),R3),
then |u| + |∇d| /∈ Lq([0, T], Lp(R3)), where p and q safisfy the Ladyzhenskaya-Prodi-Serrin´s condition: 3/p+2/q= 1 and p ∈ (3,+∞].

Key words: incompressible nematic liquid crystal flow, Ladyzhenskaya-Prodi-Serrin´s cri-terion

中图分类号: 

  • 35Q35