论文标题
随机埃里克森（Ericksen）的全球弱解决方案 - 维度二
Global weak solutions to the Stochastic Ericksen--Leslie equations in dimension two
论文作者
论文摘要
我们为简化的随机Ericksen建立了弱的Martingale解决方案的全球存在 - LESLIE系统，建模由二维有界域上的Wiener-Type噪声驱动的列液晶流。解决方案的构建是基于金茨堡 - landau近似值的收敛性。为了实现这种收敛，我们首先根据Pohozaev型参数利用Ericksen应力张量场的浓度 - 癌化方法，其次是基于均匀能量估计的Skorokhod紧凑型定理。
We establish the global existence of weak martingale solutions to the simplified stochastic Ericksen--Leslie system modeling the nematic liquid crystal flow driven by Wiener-type noises on the two-dimensional bounded domains. The construction of solutions is based on the convergence of Ginzburg--Landau approximations. To achieve such a convergence, we first utilize the concentration-cancellation method for the Ericksen stress tensor fields based on a Pohozaev type argument, and second the Skorokhod compactness theorem, which is built upon a uniform energy estimate.
