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

Giacomo Canevari (1)

1 LJLL - Laboratoire Jacques-Louis Lions

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.

Mots clés: Landau-de Gennes model; Q-tensor; convergence; biaxiality

Domaines: Equations aux dérivées partielles [math.AP]

Giacomo Canevari. Biaxiality in the asymptotic analysis of a 2D Landau-de Gennes model for liquid crystals. 2013. ⟨hal-00925887⟩