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

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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https://hal.archives-ouvertes.fr/hal-02265222
Contributor : Radu Ignat <>
Submitted on : Thursday, August 8, 2019 - 6:58:37 PM
Last modification on : Sunday, August 11, 2019 - 1:09:06 AM

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  • HAL Id : hal-02265222, version 1
  • ARXIV : 1908.00033

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Radu Ignat, Luc Nguyen, Valeriy Slastikov, Arghir Zarnescu. Symmetry and multiplicity of solutions in a two-dimensional Landau-de Gennes model for liquid crystals. 2019. ⟨hal-02265222⟩

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