论文标题
与随机力的可压缩液晶系统的强溶液
Strong solution for compressible liquid crystal system with random force
论文作者
论文摘要
我们研究了三维可压缩的Navier-Stokes方程，再加上$ Q $ -TENSOR方程，该方程受到乘法随机力的扰动，该力描述了列液晶流动的运动。在PDE和概率方面都是``强度''在``强度'''''''''强度和概率方面都建立了当地的存在和唯一性，并建立了``强度''''''''''''强度和概率意义。证明取决于盖尔金近似方案，紧凑性，极限的识别，限制，唯一性，唯一性和削减参数。耦合系统的复杂结构，高阶项目的估计值也是文章中的挑战性部分。
We study the three-dimensional compressible Navier-Stokes equations coupled with the $Q$-tensor equation perturbed by a multiplicative stochastic force, which describes the motion of nematic liquid crystal flows. The local existence and uniqueness of strong pathwise solution up to a positive stopping time is established where ``strong" is in both PDE and probability sense. The proof relies on the Galerkin approximation scheme, stochastic compactness, identification of the limit, uniqueness and a cutting-off argument. In the stochastic setting, we develop an extra layer approximation to overcome the difficulty arising from the stochastic integral while constructing the approximate solution. Due to the complex structure of the coupled system, the estimates of the high-order items are also the challenging part in the article.
