This article is devoted to the study of the so-called incompressible limit for solutions of the compressible liquid crystals system. We consider the problem in the whole space R^N and a bounded domain of R^N with Diri...This article is devoted to the study of the so-called incompressible limit for solutions of the compressible liquid crystals system. We consider the problem in the whole space R^N and a bounded domain of R^N with Dirichlet boundary conditions. Here we set the number of dimension N = 2 or 3.展开更多
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 o...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,＋∞].展开更多
基金supported by National Natural Science Foundation of China-NSAF: 11071043, 11131005
文摘This article is devoted to the study of the so-called incompressible limit for solutions of the compressible liquid crystals system. We consider the problem in the whole space R^N and a bounded domain of R^N with Dirichlet boundary conditions. Here we set the number of dimension N = 2 or 3.
基金Supported by National Natural Science Foundation of China (10976026, 11271305, 11301439, 11226174)
文摘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,＋∞].
