LPS'S CRITERION FOR INCOMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOWS  

作　　者：陈卿 谭忠 吴国春 

机构地区：[1]Department of Mathematics and Physics,Xiamen University of Technology [2]School of Mathematical Sciences,Xiamen University

出　　处：《Acta Mathematica Scientia》2014年第4期1072-1080,共9页数学物理学报（B辑英文版）

基　　金：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 R^3. We show that if 0 〈 T 〈 ＋∞ is the maximal time interval for the unique smooth solution u ∈ C^∞（[0, T）,R^3）,then ｜u｜＋｜△d｜∈L^q（[0,T],L^p（R^3））,where p and q satisfy the Ladyzhenskaya-Prodi-Serrin＇s condition：3/p＋2/q=1 and p∈（3,＋∞].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 R^3. We show that if 0 〈 T 〈 ＋∞ is the maximal time interval for the unique smooth solution u ∈ C^∞（[0, T）,R^3）,then ｜u｜＋｜△d｜∈L^q（[0,T],L^p（R^3））,where p and q satisfy 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 criterion 

分 类 号：O753.2[理学—晶体学] O357.1