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

Canevari, Giacomo

ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 1, pp. 101-137

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.

Classification : 35J25, 35J61, 35B40, 35Q70
Keywords: Landau−de Gennes model, Q-tensor, convergence, biaxiality

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