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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Cited by in corpus (4)

• Topological singular set of vector-valued maps, II: $\Gamma$-convergence for Ginzburg-Landau type functionals
• Tetrahedral frame fields via constrained third order symmetric tensors
• Torus-like solutions for the Landau-de Gennes model. Part III: torus vs split minimizers
• A variational singular perturbation problem motivated by Ericksen's model for nematic liquid crystals