Symmetry and multiplicity of solutions in a two-dimensional Landau-de Gennes model for liquid crystals

Author: 

Ignat, R
Nguyen, L
Slastikov, V
Zarnescu, A

Publication Date: 

20 May 2020

Journal: 

Archive for Rational Mechanics and Analysis

Last Updated: 

2021-04-30T19:37:32.12+01:00

Issue: 

3

Volume: 

237

DOI: 

10.1007/s00205-020-01539-x

page: 

1421-1473

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.

Symplectic id: 

1105091

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article