{
  "id": "0911.5032",
  "version": "v1",
  "published": "2009-11-26T08:52:55.000Z",
  "updated": "2009-11-26T08:52:55.000Z",
  "title": "On a non-isothermal model for nematic liquid crystals",
  "authors": [
    "E. Feireisl",
    "E. Rocca",
    "G. Schimperna"
  ],
  "journal": "Nonlinearity, 24 (2011), 243-257",
  "categories": [
    "math.AP"
  ],
  "abstract": "A model describing the evolution of a liquid crystal substance in the nematic phase is investigated in terms of three basic state variables: the {\\it absolute temperature} $\\teta$, the {\\it velocity field} $\\ub$, and the {\\it director field} $\\bd$, representing preferred orientation of molecules in a neighborhood of any point of a reference domain. The time evolution of the velocity field is governed by the incompressible Navier-Stokes system, with a non-isotropic stress tensor depending on the gradients of the velocity and of the director field $\\bd$, where the transport (viscosity) coefficients vary with temperature. The dynamics of $\\bd$ is described by means of a parabolic equation of Ginzburg-Landau type, with a suitable penalization term to relax the constraint $|\\bd | = 1$. The system is supplemented by a heat equation, where the heat flux is given by a variant of Fourier's law, depending also on the director field $\\bd$. The proposed model is shown compatible with \\emph{First and Second laws} of thermodynamics, and the existence of global-in-time weak solutions for the resulting PDE system is established, without any essential restriction on the size of the data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-26T08:52:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76A15",
      "74G25"
    ],
    "keywords": [
      "nematic liquid crystals",
      "non-isothermal model",
      "director field",
      "velocity field",
      "global-in-time weak solutions"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/24/1/012",
      "journal": "Nonlinearity",
      "year": 2011,
      "month": "Jan",
      "volume": 24,
      "number": 1,
      "pages": 243
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011Nonli..24..243F"
    }
  }
}