On strong solution to the 2D stochastic Ericksen-Leslie system: A Ginzburg-Landau approximation approach

Existence, uniqueness and regularity for the stochastic Ericksen-Leslie equation

We investigate existence and uniqueness for the stochastic liquid crystal flow driven by colored noise on the two-dimensional torus. After giving a natural uniqueness criterion, we prove local solvability in $L^p$-based spaces, for every $p>2.$ Thanks to a bootstrap principle together with a Gyöngy-Krylov-type compactness argument, this will ultimately lead us to prove the existence of a particular class of global solutions which are partially regular, strong in the probabilistic sense, and taking values in the "critical space" $L^2\times H^1.$

三维随机Ericksen--Leslie方程的局部正则性

Partial Regularity for the Three-dimensional Stochastic Ericksen--Leslie equations

本文证明三维随机Ericksen-Leslie方程鞅适度弱解的奇点集一维抛物型Hausdorff测度为零，通过构造局部能量保持逼近和爆破论证实现。