论文标题
关于2D随机埃里克森 - 莱斯系统的强大解决方案：Ginzburg-Landau近似方法
On strong solution to the 2D stochastic Ericksen-Leslie system: A Ginzburg-Landau approximation approach
论文作者
论文摘要
在此手稿中，我们考虑了一个高度非线性和约束的随机PDE，该PDE在随机扰动下对二维列液晶的动力学进行了建模。该SPDES系统也称为随机Ericksen-Leslie方程（SELES）。我们讨论了随机Ericksen-Leslie方程的局部强大解决方案的存在。特别是，我们研究了SELES的随机Ginzburg-landau近似，并证明具有$ \ sh^1 \ times \ sh^2 $的初始数据的SELE至少具有themingale，至少具有一种局部局部解决方案，在PDES Sense中很强。
In this manuscript, we consider a highly nonlinear and constrained stochastic PDEs modelling the dynamics of 2-dimensional nematic liquid crystals under random perturbation. This system of SPDEs is also known as the stochastic Ericksen-Leslie equations (SELEs). We discuss the existence of local strong solution to the stochastic Ericksen-Leslie equations. In particular, we study the convergence the stochastic Ginzburg-Landau approximation of SELEs, and prove that the SELEs with initial data in $\sh^1\times \sh^2$ has at least a martingale, local solution which is strong in PDEs sense.
