{
  "id": "1408.4146",
  "version": "v1",
  "published": "2014-08-18T20:17:13.000Z",
  "updated": "2014-08-18T20:17:13.000Z",
  "title": "Global existence of weak solutions of the nematic liquid crystal flow in dimensions three",
  "authors": [
    "Fanghua Lin",
    "Changyou Wang"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "For any bounded smooth domain $\\Omega\\subset\\mathbb R^3$, we establish the global existence of a weak solution $u:\\Omega\\times (0,+\\infty)\\to\\mathbb R^3\\times\\mathbb S^2$ of the initial-boundary value (or the Cauchy) problem of the simplified Ericksen-Leslie system (1.1) modeling the hydrodynamic flow of nematic liquid crystals for any initial and boundary (or Cauchy) data $(u_0. d_0)\\in {\\bf H}\\times H^1(\\Omega,\\mathbb S^2$), with $d_0(\\Omega)\\subset\\mathbb S^2_+$ (the upper hemisphere). Furthermore, ($u,d$) satisfies the global energy inequality (1.4).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-18T20:17:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nematic liquid crystal flow",
      "global existence",
      "weak solution",
      "dimensions",
      "global energy inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.4146L"
    }
  }
}