Biaxiality in the asymptotic analysis of a 2D Landau−de Gennes model for liquid crystals

Sorbonne Universités, UPMC – Université Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France
canevari@ann.jussieu.fr

Received: 16 December 2013
Revised: 12 May 2014

Abstract

We consider the Landau−de Gennes variational problem on a bounded, two dimensional domain, subject to Dirichlet smooth boundary conditions. We prove that minimizers are maximally biaxial near the singularities, that is, their biaxiality parameter reaches the maximum value 1. Moreover, we discuss the convergence of minimizers in the vanishing elastic constant limit. Our asymptotic analysis is performed in a general setting, which recovers the Landau−de Gennes problem as a specific case.