Radial symmetry on three-dimensional shells in the Landau-de Gennes theory

Canevari, Giacomo and Ramaswamy, Mythily and Majumdar, Apala (2016) Radial symmetry on three-dimensional shells in the Landau-de Gennes theory. Physica D: Nonlinear Phenomena, 314. pp. 18-34. ISSN 0167-2789 (https://doi.org/10.1016/j.physd.2015.09.013)

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Abstract

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.

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