Global well-posedness for the dynamical Q-tensor model of liquid crystals  

作　　者：HUANG JinRui DING ShiJin 

机构地区：[1]School of Mathematics and Computational Science, Wuyi University [2]School of Mathematical Sciences, South China Normal University

出　　处：《Science China Mathematics》2015年第6期1349-1366,共18页中国科学：数学（英文版）

基　　金：supported by National Basic Research Program of China(973 Program)(Grant No.2011CB808002);National Natural Science Foundation of China(Grant Nos.11071086,11371152,11401439 and 11128102);the Natural Science Foundation of Guangdong Province(Grant No.S2012010010408);the Foundation for Distinguished Young Talents in Higher Education of Guangdong(Grant No.2014KQNCX162);the University Special Research Foundation for Ph.D Program(Grant No.20104407110002);the Science Foundation for Young Teachers of Wuyi University(Grant No.2014zk06)

摘　　要：We consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in dimension three. Furthermore, the global well-posedness of strong solutions is studied with sufficiently large viscosity of fluid. Finally, we show a continuous dependence result on the initial data which directly yields the weak-strong uniqueness of solutions.We consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in dimension three. Furthermore, the global well-posedness of strong solutions is studied with sufficiently large viscosity of fluid. Finally, we show a continuous dependence result on the initial data which directly yields the weak-strong uniqueness of solutions.

关 键 词：dynamical tensor Stokes parabolic nematic viscosity Navier estimates uniqueness proof 

分 类 号：O35[理学—流体力学] O175[理学—力学]