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arXiv · 1908.00033

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

Radu Ignat·Luc Nguyen·Valeriy Slastikov·Arghir Zarnescu
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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 $\frac{k}{2}$ for some given {\bf 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.

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Radu Ignat, Luc Nguyen, Valeriy Slastikov, Arghir Zarnescu. 2019-07-31. Symmetry and multiplicity of solutions in a two-dimensional Landau-de Gennes model for liquid crystals. https://doi.org/10.1007/s00205-020-01539-x

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