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
Revised: 12 May 2014
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.
Mathematics Subject Classification: 35J25 / 35J61 / 35B40 / 35Q70
Key words: Landau−de Gennes model / Q-tensor / convergence / biaxiality
© EDP Sciences, SMAI, 2014