BIAXIALITY IN THE ASYMPTOTIC ANALYSIS OF A 2D LANDAU-DE GENNES MODEL FOR LIQUID CRYSTALS

被引：47
|
作者：
Canevari, Giacomo [1 ]
机构：
[1] Univ Paris 06, Sorbonne Univ, UMR 7598, Lab Jacques Louis Lions, F-75005 Paris, France
来源：
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2015年 / 21卷 / 01期
关键词：
Landau-de Gennes model; Q-tensor; convergence; biaxiality; PARTIAL REGULARITY; MINIMIZERS; EXISTENCE; ENERGY;
D O I：
10.1051/cocv/2014025
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
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.
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页码：101 / 137
页数：37
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