Existence of regular solutions to the full Liquid Crystal System

TL;DR

This paper proves the global regularity of solutions to the full Liquid Crystal System in 2D for general data and in 3D for small or short-time data, also establishing a weak-strong uniqueness result.

Contribution

It demonstrates the existence of regular solutions to the full Liquid Crystal System under various conditions, including general data in 2D and small data in 3D, extending previous results.

Findings

Global regularity in 2D for general data

Global regularity in 3D for small data

Weak-strong uniqueness of solutions

Abstract

We study the general Ericksen-Leslie system with non-constant density, which describes the flow of nematic liquid crystal. In particular the model investigated here is associated with Parodi's relation. We prove that: in two dimension, the solutions are globally regular with general data; in three dimension, the solutions are globally regular with small initial data, or for short time with large data. Moreover, a weak-strong type of uniqueness result is obtained.