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 R 3 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].

The stochastic Landau–Lifshitz–Bloch equation describes the phase spins in a ferromagnetic material and has a significant role in simulating heat-assisted magnetic recording. In this paper, we consider the deviation of the solution to the 1D stochastic Landau–Lifshitz–Bloch equation, that is, we give the asymptotic behavior of the trajectory uε−u0ελ(ε) as ɛ → 0+, for λ(ε)=1ε and 1, respectively. In other words, the large deviation principle and the central limit theorem are established, respectively.

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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 bounded domain in R 3 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 [9].