Martingale solution for stochastic active liquid crystal system

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 smooth bounded domain \begin{document}$ \mathbb{R}^{3} $\end{document} with large initial data. The coupled structure makes the analysis challenging, and more delicate arguments are required case compared deterministic one [11].