{
  "id": "1303.4488",
  "version": "v2",
  "published": "2013-03-19T05:20:39.000Z",
  "updated": "2013-03-20T04:58:31.000Z",
  "title": "Blow-up criteria of strong solutions to the Ericksen-Leslie system in $\\Bbb R^3$",
  "authors": [
    "Min-Chun Hong",
    "Jinkai Li",
    "Zhouping Xin"
  ],
  "comment": "39 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we establish the local well-posedness and blow-up criteria of strong solutions to the Ericksen-Leslie system in $\\Bbb R^3$ for the well-known Oseen-Frank model. The local existence of strong solutions to liquid crystal flows is obtained by using the Ginzburg-Landau approximation approach to guarantee the constraint that the direction vector of the fluid is of length one. We establish four kinds of blow-up criteria, including (i) the Serrin type; (ii) the Beal-Kato-Majda type; (iii) the mixed type, i.e., Serrin type condition for one field and Beal-Kato-Majda type condition on the other one; (iv) a new one, which characterizes the maximal existence time of the strong solutions to the Ericksen-Leslie system in terms of Serrin type norms of the strong solutions to the Ginzburg-Landau approximate system. Furthermore, we also prove that the strong solutions of the Ginzburg-Landau approximate system converge to the strong solution of the Ericksen-Leslie system up to the maximal existence time.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-20T04:58:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "strong solution",
      "ericksen-leslie system",
      "blow-up criteria",
      "maximal existence time",
      "type condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.4488H"
    }
  }
}