{
  "id": "1411.5387",
  "version": "v1",
  "published": "2014-11-19T21:22:21.000Z",
  "updated": "2014-11-19T21:22:21.000Z",
  "title": "A uniqueness and regularity criterion for Q-tensor models with Neumann boundary conditions",
  "authors": [
    "Francisco Guillén-González",
    "María Ángeles Rodríguez-Bellido"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We give a regularity criterion for a $Q$-tensor system modeling a nematic Liquid Crystal, under homogeneous Neumann boundary conditions for the tensor $Q$. Starting of a criterion only imposed on the velocity field ${\\bf u}$ two results are proved; the uniqueness of weak solutions and the global in time weak regularity for the time derivative $(\\partial_t {\\bf u},\\partial_t Q)$. This paper extends the work done in [F. Guill\\'en-Gonz\\'alez, M.A. Rodr\\'iguez-Bellido \\& M.A. Rojas-Medar, Sufficient conditions for regularity and uniqueness of a 3D nematic liquid crystal model, Math. Nachr. 282 (2009), no. 6, 846-867] for a nematic Liquid Crystal model formulated in $({\\bf u},{\\bf d})$, where ${\\bf d}$ denotes the orientation vector of the liquid crystal molecules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-19T21:22:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35K51",
      "35Q35",
      "76A15",
      "76D03"
    ],
    "keywords": [
      "neumann boundary conditions",
      "regularity criterion",
      "q-tensor models",
      "uniqueness",
      "liquid crystal model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.5387G"
    }
  }
}