Journal
PHYSICA D-NONLINEAR PHENOMENA
Volume 314, Issue -, Pages 18-34Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physd.2015.09.013
Keywords
Nematic liquid crystals; Landau-de Gennes theory; Radial-hedgehog; Minimizing configurations; Stable configurations
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Funding
- EPSRC [EP/J001686/1, EP/J001686/2]
- OCIAM Visiting Fellowship
- Keble Advanced Studies Centre
- Royal Society International Exchange Grant [IE121157]
- University of Bath [VB-MA3AAM]
- Royal Society International Exchange Grant
- Department for Mathematical Sciences, Bath
- Engineering and Physical Sciences Research Council [EP/J001686/2, EP/J001686/1] Funding Source: researchfish
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We study the radial-hedgehog solution on a three-dimensional (3D) spherical shell with radial boundary conditions, within the Landau-de Gennes theory for nematic liquid crystals. We prove that the radial-hedgehog solution is the unique minimizer of the Landau-de Gennes energy in two separate regimes: (i) for thin shells when the temperature is below the critical nematic supercooling temperature and (ii) for a fixed shell width at sufficiently low temperatures. In case (i), we provide explicit geometry-dependent criteria for the global minimality of the radial-hedgehog solution. (C) 2015 Elsevier B.V. All rights reserved.
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