Uniqueness of Weak Solutions of the Full Coupled Navier-Stokes and Q-Tensor System in 2D

Abstract

This paper is devoted to the full system of incompressible liquid crystals, as modeled in the Q-tensor framework. The main purpose is to establish the uniqueness of weak solutions in a two dimensional setting, without imposing an extra regularity on the solutions themselves. This result only requires the initial data to fulfill the features which allow the existence of a weak solution. Thus, we also present a revisit of the global existence result in dimension two and three.