{
  "id": "1107.5445",
  "version": "v1",
  "published": "2011-07-27T11:42:03.000Z",
  "updated": "2011-07-27T11:42:03.000Z",
  "title": "On the long-time behavior of some mathematical models for nematic liquid crystals",
  "authors": [
    "Hana Petzeltová",
    "Elisabetta Rocca",
    "Giulio Schimperna"
  ],
  "journal": "Calc. Var., 46 (2013), 623-639",
  "categories": [
    "math.AP"
  ],
  "abstract": "A model describing the evolution of a liquid crystal substance in the nematic phase is investigated in terms of two basic state variables: the {\\it velocity field} $\\bu$ and the {\\it director field} $\\di$, representing the preferred orientation of molecules in a neighborhood of any point in a reference domain. After recalling a known existence result, we investigate the long-time behavior of weak solutions. In particular, we show that any solution trajectory admits a non-empty $\\omega$-limit set containing only stationary solutions. Moreover, we give a number of sufficient conditions in order that the $\\omega$-limit set contains a single point. Our approach improves and generalizes existing results on the same problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-07-27T11:42:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nematic liquid crystals",
      "long-time behavior",
      "mathematical models",
      "basic state variables",
      "solution trajectory admits"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.5445P"
    }
  }
}