Concentration-cancellation in the Ericksen-Leslie model

TL;DR

This paper proves the subconvergence of weak solutions from a Ginzburg-Landau approximation to the Ericksen-Leslie model for nematic liquid crystals, using concentration-cancellation methods to establish global-in-time weak solutions.

Contribution

It introduces a novel application of concentration-cancellation techniques to analyze the Ericksen-Leslie model, extending the understanding of weak solution stability.

Findings

Weak solutions subconverge to global-in-time solutions

Application of concentration-cancellation methods to liquid crystal models

Establishment of stability results for the Ericksen-Leslie model

Abstract

We establish the subconvergence of weak solutions to the Ginzburg-Landau approximation to global-in-time weak solutions of the Ericksen-Leslie model for nematic liquid crystals on the torus $\mathbb{T}^2$. The key argument is a variation of concentration-cancellation methods originally introduced by DiPerna and Majda to investigate the weak stability of solutions to the (steady-state) Euler equations.