{
  "id": "1205.2534",
  "version": "v1",
  "published": "2012-05-11T14:19:50.000Z",
  "updated": "2012-05-11T14:19:50.000Z",
  "title": "Trajectory attractors for the Sun-Liu model for nematic liquid crystals in 3D",
  "authors": [
    "Sergio Frigeri",
    "Elisabetta Rocca"
  ],
  "comment": "32 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove the existence of a trajectory attractor (in the sense of V.V. Chepyzhov and M.I. Vishik) for a nonlinear PDE system coming from a 3D liquid crystal model accounting for stretching effects. The system couples a nonlinear evolution equation for the director d (introduced in order to describe the preferred orientation of the molecules) with an incompressible Navier-Stokes equation for the evolution of the velocity field u. The technique is based on the introduction of a suitable trajectory space and of a metric accounting for the double-well type nonlinearity contained in the director equation. Finally, a dissipative estimate is obtained by using a proper integrated energy inequality. Both the cases of (homogeneous) Neumann and (non-homogeneous) Dirichlet boundary conditions for d are considered.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-11T14:19:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nematic liquid crystals",
      "trajectory attractor",
      "sun-liu model",
      "3d liquid crystal model accounting",
      "proper integrated energy inequality"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1088/0951-7715/26/4/933",
      "journal": "Nonlinearity",
      "year": 2013,
      "month": "Apr",
      "volume": 26,
      "number": 4,
      "pages": 933
    },
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013Nonli..26..933F"
    }
  }
}