Global Weak Solutions to a General Liquid Crystals System

TL;DR

This paper establishes the existence of global weak solutions with finite energy for a broad class of liquid crystal models in both bounded and unbounded three-dimensional domains.

Contribution

It proves the global existence of weak solutions for a general liquid crystals system, extending previous results to more comprehensive models and settings.

Findings

Existence of finite energy weak solutions in bounded domains.

Existence of finite energy weak solutions in the whole space.

Applicable to a broad class of liquid crystal models.

Abstract

We prove the global existence of finite energy weak solutions to the general liquid crystals system. The problem is studied in bounded domain of $R^3$ with Dirichlet boundary conditions and the whole space $R^3$.