Large Deviations for Stochastic Nematic Liquid Crystals Driven by Multiplicative Gaussian Noise

Abstract

In this paper, we prove the existence of a unique maximal local strong solutions to a stochastic system for both 2D and 3D penalised nematic liquid crystals driven by multiplicative Gaussian noise. In the 2D case, we show that this solution is global. As a by-product of our investigation, but of independent interest, we present a general method based on fixed point arguments to establish the existence and uniqueness of a maximal local solution of an abstract stochastic evolution equations with coefficients satisfying local Lipschitz condition involving the norms of two different Banach spaces.

On the existence of weak martingale solution for stochastic non-homogeneous penalised nematic liquid crystal system

“…As for the stochastic version, Z. Brzézniak, E. Hausenblas and P. Razafimandimby [2] built the global existence and uniqueness of strong solution and the existence of weak solution in 2-dimensional case, and the local maximal pathwise solution in 3-dimensional case corresponding to the Wiener noise, then the first author, U. Manna and A. Panda [3,4] extended these results to the case of pure jump noise and built the large deviation principle. B. Guo, G. Zhou and W. Zhou [14] considered the long-term behaviour of the system with multiplicative noise.…”