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

[img]
Preview
Text (Canevari-etal-PNP2016-Radial-symmetry-three-dimensional-shells-Landau-de-Gennes-theory)
Canevari_etal_PNP2016_Radial_symmetry_three_dimensional_shells_Landau_de_Gennes_theory.pdf
Accepted Author Manuscript
License: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 logo

Download (250kB)| Preview

    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.