{
  "id": "1703.02214",
  "version": "v1",
  "published": "2017-03-07T05:13:22.000Z",
  "updated": "2017-03-07T05:13:22.000Z",
  "title": "Well-posedness of the Ericksen-Leslie System for the Oseen-Frank Model in L^3_{uloc}(\\mathbb{R}^3)",
  "authors": [
    "Min-Chun Hong",
    "Yu Mei"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate the Ericksen-Leslie system for the Oseen-Frank model with unequal Frank elastic constants in $\\mathbb{R}^3$. To generalize the result of Hineman-Wang \\cite{HW}, we prove existence of solutions to the Ericksen-Leslie system with initial data having small $L^3_{uloc}$-norm. In particular, we use a new idea to obtain a local $L^3$-estimate through interpolation inequalities and a covering argument, which is different from the one in \\cite{HW}. Moreover, for uniqueness of solutions, we find a new way to remove the restriction on the Frank elastic constants by using the rotation invariant property of the Oseen-Frank density. We combine this with a method of Li-Titi-Xin \\cite{LTX} to prove uniqueness of the $L^3_{uloc}$-solutions of the Ericksen-Leslie system assuming that the initial data has a finite energy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-07T05:13:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ericksen-leslie system",
      "oseen-frank model",
      "unequal frank elastic constants",
      "well-posedness",
      "initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}