Symmetry of uniaxial global Landau-de Gennes minimizers in the theory of nematic liquid crystals

Details Symmetry of uniaxial global Landau-de Gennes minimizers in the theory of nematic liquid crystals Symmetry of uniaxial global Landau-de Gennes minimizers in the theory of nematic liquid crystals

2011-10-28

arxiv.org/abs/1110.6414v1

Mathematics

Analysis of PDEs

Scientific paper

We study uniaxial energy-minimizers within the Landau-de Gennes theory for nematic liquid crystals on a three-dimensional spherical droplet subject to homeotropic boundary conditions. We work in the low-temperature regime and show that uniaxial energy-minimizers necessarily have the structure of the well-studied radial-hedgehog solution in the low-temperature limit. An immediate consequence of this result is that Landau-de Gennes energy minimizers cannot be purely uniaxial for sufficiently low temperatures.

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