{
  "id": "1805.02439",
  "version": "v1",
  "published": "2018-05-07T10:57:45.000Z",
  "updated": "2018-05-07T10:57:45.000Z",
  "title": "Convergence to equilibrium of global weak solutions for a Q-tensor problem related to liquid crystals",
  "authors": [
    "Blanca Climent-Ezquerra",
    "Francisco Guillén-González"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a Q-tensor problem modeling the dynamic of nematic liquid crystals in 3D domains. The system consists of the Navier-Stokes equations, with an extra stress tensor depending on the elastic forces of the liquid crystal, coupled with an Allen-Cahn system for the Q-tensor variable. This problem has a dissipative in time free-energy which leads, in particular, to prove the existence of global in time weak solutions. We analyze the large-time behavior of the weak solutions. By using a Lojasiewicz-Simon's result, we prove the convergence as time goes to infinity of the whole trajectory to a single equilibrium.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-07T10:57:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35D30",
      "35K55",
      "35Q30",
      "35Q35",
      "76A15",
      "76D05"
    ],
    "keywords": [
      "global weak solutions",
      "q-tensor problem",
      "convergence",
      "nematic liquid crystals",
      "time weak solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}