Global Existence of Weak Solutions to the Two Dimensional Nematic Liquid Crystal Flow with Partially Free Boundary

TL;DR

This paper proves the global existence of weak solutions with partial regularity for a 2D nematic liquid crystal flow with partially free boundary, including regularity estimates and a uniqueness result.

Contribution

It establishes the first global existence and regularity results for weak solutions to 2D nematic liquid crystal flow with partially free boundary.

Findings

Global existence of weak solutions

Partial regularity properties proven

Uniqueness of solutions established

Abstract

We consider a nematic liquid crystal flow with partially free boundary in a smooth bounded domain in $\mathbb{R}^2$. We prove regularity estimates and the global existence of weak solutions enjoying partial regularity properties, and a uniqueness result.