Stochastic Analysis of Nematic Liquid Crystals

In this talk, I will be discussing the results obtained for the stochastic evolution equation, which describes the system governing the nematic liquid crystals perturbed by pure jump noise in the Marcus canonical form.

A briefing on the existence of a martingale solution in two and three dimensions will be presented. In addition, the pathwise uniqueness of the martingale solution in two dimensions will be presented, from which the existence of a strong solution will be deduced.

The final part of the talk concerns the large deviation theory for the above-said model. I start with the stochastic two-dimensional nematic liquid crystal model influenced by multiplicative Gaussian noise. The Wentzell-Freidlin type large deviations principle for the small noise asymptotic of solutions will be analyzed using the weak convergence method. Then using a similar technique, I will establish a large deviation principle for stochastic nematic liquid crystals driven by pure jump noise in the Marcus canonical form in two dimensions.