{
  "id": "1211.5866",
  "version": "v2",
  "published": "2012-11-26T06:17:03.000Z",
  "updated": "2013-12-02T14:10:54.000Z",
  "title": "Global Existence of Strong Solutions to Incompressible MHD",
  "authors": [
    "Huajun Gong",
    "Jinkai Li"
  ],
  "comment": "10 pages. Communications on Pure and Applied Analysis, 2014",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We establish the global existence and uniqueness of strong solutions to the initial boundary value problem for incompressible MHD equations in a bounded smooth domain of three spatial dimensions with initial density being allowed to have vacuum, in particular, the initial density can vanish in a set of positive Lebessgue measure. More precisely, under the assumption that the production of the quantities $|\\sqrt\\rho_0u_0|_{L^2(\\Omega)}^2+|H_0|_{L^2(\\Omega)}^2$ and $|\\nabla u_0|_{L^2(\\Omega)}^2+|\\nabla H_0|_{L^2(\\Omega)}^2$ is suitably small, with the smallness depending only on the bound of the initial density and the domain, we prove that there is a unique strong solution to the Dirichlet problem of the incompressible MHD system.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-02T14:10:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global existence",
      "initial density",
      "initial boundary value problem",
      "unique strong solution",
      "incompressible mhd equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.5866G"
    }
  }
}