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arXiv · 1307.8065

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

Giacomo Canevari
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Abstract

We consider the Landau-de Gennes variational problem on a bound\-ed, 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.

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Giacomo Canevari. 2014-01-08. Biaxiality in the asymptotic analysis of a 2-D Landau-de Gennes model for liquid crystals. https://arxiv.org/abs/1307.8065

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