{
  "id": "2109.15178",
  "version": "v2",
  "published": "2021-09-30T14:48:20.000Z",
  "updated": "2022-02-23T16:01:57.000Z",
  "title": "Torus-like solutions for the Landau-de Gennes model. Part III: torus vs split minimizers",
  "authors": [
    "Federico Dipasquale",
    "Vincent Millot",
    "Adriano Pisante"
  ],
  "comment": "Presentation greatly improved. Theorem 1.3 and Theorem 1.4 also improved. Corollary 6.12 added",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the behaviour of global minimizers of a continuum Landau-de Gennes energy functional for nematic liquid crystals, in three-dimensional axially symmetric domains domains diffeomorphic to a ball (a nematic droplet) and in a restricted class of $\\bbS^1$-equivariant configurations. It is known from our previous paper \\cite{DMP2} that, assuming smooth and uniaxial (e.g. homeotropic) boundary conditions and a physically relevant norm constraint in the interior (Lyuksyutov constraint), minimizing configurations are either of \\emph{torus} or of \\emph{split} type. Here, starting from a nematic droplet with the homeotropic boundary condition, we show how singular (split) solutions or smooth (torus) solutions (or even both) for the Euler-Lagrange equations do appear as energy minimizers by suitably deforming either the domain or the boundary data. As a consequence, when minimizers among $\\bbS^1$-equivariant configurations are singular we derive symmetry breaking result for the minimization among all competitors.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-02-23T16:01:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J50",
      "35B40",
      "82D30",
      "76A15"
    ],
    "keywords": [
      "landau-de gennes model",
      "symmetric domains domains diffeomorphic",
      "split minimizers",
      "axially symmetric domains domains",
      "torus-like solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}