Convergence of Ginzburg-Landau Approximations for a Liquid Crystal Flow in 2D

TL;DR

This paper proves the long-term convergence of a Ginzburg-Landau approximation for a 2D liquid crystal flow model, characterizes singularities, and shows they are finitely many.

Contribution

It establishes convergence and singularity characterization for a Ginzburg-Landau approximation of a liquid crystal flow in two dimensions.

Findings

Convergence of the approximation for all time

Finite number of singular points

Characterization of singularities

Abstract

In this paper we prove the convergence for all time for a Ginzburg- Landau type approximation of a simplified Ericksen-Leslie model in two dimension. Moreover, we are able to show that the singular set consists in at most finitely many singular points and we give a characterizations of the singularities.