论文标题
2D中简化的列液流量的紧凑性弱
Weak compactness of simplified nematic liquid flows in 2D
论文作者
论文摘要
对于任何有限的，光滑的域$ω\ subset \ r^2 $，％（或$ω= \ r^2 $），我们将建立解决方案的薄弱属性，用于简化的Ericksen-Leslie系统，用于单轴和双轴和双轴和双轴夜间较弱的静态液体溶液的较弱的液体液体溶液的融合，并Ericksen-Leslie系统作为参数趋于零。这是基于Ericksen应力张量的补偿紧凑特性，该特性是由Ericksen-Leslie系统的Hopf差异的$ l^p $ esstimate获得的，以及Ginzburg-Landau型nematic液晶流的Pohozaev类型论证。
For any bounded, smooth domain $Ω\subset \R^2$, %(or $Ω=\R^2$), we will establish the weak compactness property of solutions to the simplified Ericksen-Leslie system for both uniaxial and biaxial nematics, and the convergence of weak solutions of the Ginzburg-Landau type nematic liquid crystal flow to a weak solution of the simplified Ericksen-Leslie system as the parameter tends to zero. This is based on the compensated compactness property of the Ericksen stress tensors, which is obtained by the $L^p$-estimate of the Hopf differential for the Ericksen-Leslie system and the Pohozaev type argument for the Ginzburg-Landau type nematic liquid crystal flow.
