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 solution...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.展开更多
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)+3 种基金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)
文摘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.
