It is proved that any weak solution to the initial value problem of two dimensional Landau-Lifshitz equation is unique and is smooth with the exception of at most finitely many points, provided that the weak solution ...It is proved that any weak solution to the initial value problem of two dimensional Landau-Lifshitz equation is unique and is smooth with the exception of at most finitely many points, provided that the weak solution has finite energy.展开更多
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
In two dimensions,we study the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions.As shown by Ding et al.(2013),when the parameterλ→∞,the solutions to the compressible liquid crysta...In two dimensions,we study the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions.As shown by Ding et al.(2013),when the parameterλ→∞,the solutions to the compressible liquid crystal system approximate that of the incompressible one.Furthermore,Ding et al.(2013)proved that the regular incompressible limit solution is global in time with small enough initial data.In this paper,we show that the solution to the compressible liquid crystal flow also exists for all time,provided thatλis sufciently large and the initial data are almost incompressible.展开更多
文摘It is proved that any weak solution to the initial value problem of two dimensional Landau-Lifshitz equation is unique and is smooth with the exception of at most finitely many points, provided that the weak solution has finite energy.
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.
基金supported by National Basic Research Program of China(973 Program)(Grant No.2011CB808002)National Natural Science Foundation of China(Grant Nos.11001085,11071086 and 11128102)+2 种基金the University Special Research Foundation for PhD Program(Grant No.20104407110002)the PhD Programs Foundation of Ministry of Education of China(Grant No.20100172120026)the Fundamental Research Funds for the Central Universities(Grant No.2012ZZ0075)
文摘In two dimensions,we study the compressible hydrodynamic flow of liquid crystals with periodic boundary conditions.As shown by Ding et al.(2013),when the parameterλ→∞,the solutions to the compressible liquid crystal system approximate that of the incompressible one.Furthermore,Ding et al.(2013)proved that the regular incompressible limit solution is global in time with small enough initial data.In this paper,we show that the solution to the compressible liquid crystal flow also exists for all time,provided thatλis sufciently large and the initial data are almost incompressible.
