Acta mathematica scientia, Series B >
LPS´S CRITERION FOR INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS
Received date: 2013-05-24
Online published: 2014-07-20
Supported by
The research was supported Supported by National Natural Science Foundation of China (10976026, 11271305, 11301439, 11226174).
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,+∞].
CHEN Qing , TAN Zhong , WU Guo-Chun . LPS´S CRITERION FOR INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS[J]. Acta mathematica scientia, Series B, 2014 , 34(4) : 1072 -1080 . DOI: 10.1016/S0252-9602(14)60070-9
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