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
The authors establish a Serrin＇s regularity criterion for the β-generalized dis- sipative surface quasi-geostrophic equation. More precisely, it is shown that if the smooth solution β satisfies
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,＋∞].
基金supported by the National Natural Science Foundation of China(Nos.11501453,11371294,11326155,11401202)the Fundamental Research Funds for the Central Universities(No.2014YB031)+2 种基金the Fundamental Research Project of Natural Science in Shaanxi Province–Young Talent Project(No.2015JQ1004)the Scientific Research Fund of Hunan Provincial Education Department(No.14B117)the China Postdoctoral Science Foundation(No.2015M570053)
文摘The authors establish a Serrin＇s regularity criterion for the β-generalized dis- sipative surface quasi-geostrophic equation. More precisely, it is shown that if the smooth solution β satisfies
