Existence of weak martingale solution of Nematic Liquid Crystals driven by Pure Jump Noise

TL;DR

This paper proves the existence of weak martingale solutions for stochastic nematic liquid crystal equations driven by pure jump noise in both 2D and 3D, using approximation and compactness methods.

Contribution

It establishes the existence of weak solutions for the stochastic nematic liquid crystal system driven by pure jump noise, including pathwise uniqueness and strong solutions in 2D.

Findings

Existence of weak martingale solutions in 2D and 3D

Pathwise uniqueness of solutions in 2D

Existence of strong solutions in 2D

Abstract

In this work we consider a stochastic evolution equation which describes the system governing the nematic liquid crystals driven by a pure jump noise. The existence of a martingale solution is proved for both 2D and 3D cases. The construction of the solution is based on the classical Faedo-Galerkin approximation, compactness method and the Jakubowski's version of the Skorokhod representation theorem for non-metric spaces. We prove the solution is pathwise unique and further establish the existence of a strong solution in the 2D case.