Symmetry and Multiplicity of Solutions in a Two-Dimensional Landau–de Gennes Model for Liquid Crystals

Radu Ignat, Luc Nguyen*, Valeriy Slastikov, Arghir Zarnescu

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

We consider a variational two-dimensional Landau–de Gennes model in the theory of nematic liquid crystals in a disk of radius R. We prove that under a symmetric boundary condition carrying a topological defect of degree k2 for some given even non-zero integer k, there are exactly two minimizers for all large enough R. We show that the minimizers do not inherit the full symmetry structure of the energy functional and the boundary data. We further show that there are at least five symmetric critical points.

Original languageEnglish
Pages (from-to)1421-1473
Number of pages37
JournalArchive for Rational Mechanics and Analysis
Volume237
Issue number3
Early online date20 May 2020
DOIs
Publication statusPublished - 1 Sep 2020

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