Geodesic
Biaxiality in the asymptotic analysis of a 2D Landau−de Gennes model for liquid crystals
Canevari, Giacomo1 
1 Sorbonne Universités, UPMC – Université Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 1, pp. 101-137

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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.

DOI : 10.1051/cocv/2014025
Classification : 35J25, 35J61, 35B40, 35Q70
Keywords: Landau−de Gennes model, Q-tensor, convergence, biaxiality

Canevari, Giacomo 1

1 Sorbonne Universités, UPMC – Université Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, 75005 Paris, France 
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     title = {Biaxiality in the asymptotic analysis of a {2D} {Landau\ensuremath{-}de} {Gennes} model for liquid crystals},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
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Canevari, Giacomo. Biaxiality in the asymptotic analysis of a 2D Landau−de Gennes model for liquid crystals. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 1, pp. 101-137. doi: 10.1051/cocv/2014025

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