Martingale solution for stochastic active liquid crystal system

Abstract

The global weak martingale solution is built through a four-level approximation scheme to stochastic compressible active liquid crystal system driven by multiplicative noise in a smooth bounded domain in \begin{document}$ \mathbb{R}^{3} $\end{document} with large initial data. The coupled structure makes the analysis challenging, and more delicate arguments are required in stochastic case compared to the deterministic one [ 11 ].