{
  "id": "1409.0143",
  "version": "v1",
  "published": "2014-08-30T18:35:06.000Z",
  "updated": "2014-08-30T18:35:06.000Z",
  "title": "Radial Symmetry on 3D Shells in the Landau-de Gennes Theory",
  "authors": [
    "Apala Majumdar",
    "Giacomo Canevari",
    "Mythily Ramaswamy"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the stability of 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 show that the radial-hedgehog solution has no zeroes for a sufficiently narrow shell, for all temperatures below the nematic supercooling temperature. We prove that the radial-hedgehog solution is the unique global Landau-de Gennes energy minimizer for a sufficiently narrow 3D spherical shell, for all temperatures below the nematic supercooling temperature. We provide explicit geometry-dependent criteria for the global minimality of the radial-hedgehog solution in this temperature regime. In the low temperature limit, we prove the local stability of the radial-hedgehog solution on a 3D spherical shell, for all values of the inner and outer radii.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-30T18:35:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "35J20",
      "35B06",
      "76A15"
    ],
    "keywords": [
      "landau-de gennes theory",
      "radial-hedgehog solution",
      "3d shells",
      "radial symmetry",
      "narrow 3d spherical shell"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.0143M"
    }
  }
}