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

TL;DR

This paper proves the uniqueness of weak solutions for the 2D incompressible liquid crystal system modeled by Q-tensors, without extra regularity assumptions, and revisits global existence results.

Contribution

It establishes the uniqueness of weak solutions in 2D for the full coupled Navier-Stokes and Q-tensor system without additional regularity requirements.

Findings

Uniqueness of weak solutions in 2D established

Revisit of global existence results in 2D and 3D

No extra regularity needed for initial data

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.