Concentration-cancellation in 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.