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Line defects in the vanishing elastic constant limit of a three-dimensional Landau-de Gennes model

By Giacomo Canevari

Abstract

62 pages, 4 figures.We consider the Landau-de Gennes variational model for nematic liquid crystals, in three-dimensional domains. We are interested in the asymptotic behaviour of minimizers as the elastic constant tends to zero. Assuming that the energy of minimizers is bounded by the logarithm of the elastic constant, there exists a relatively closed, 1-rectiable set S line of nite length, such that minimizers converge to a locally harmonic map away from S line. We provide sucient conditions for the logarithmic energy bound to be satised. Finally, we show by an example that the limit map may have both point and line singularities

Topics: Landau-de Gennes model, Q-tensors, asymptotic analysis, topological singularities, line defects, rectiable sets, 2010 MSC: 76A15, 35J57, 35B40, 35A20, [ MATH.MATH-AP ] Mathematics [math]/Analysis of PDEs [math.AP]
Publisher: HAL CCSD
Year: 2015
OAI identifier: oai:HAL:hal-01157753v1
Provided by: Hal-Diderot

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