{
  "id": "math/0611165",
  "version": "v4",
  "published": "2006-11-07T08:19:25.000Z",
  "updated": "2007-03-13T12:20:10.000Z",
  "title": "Existence theorem and blow-up criterion of strong solutions to the two-fluid MHD equation in ${\\mathbb R}^3$",
  "authors": [
    "Qionglei Chen",
    "Changxing Miao"
  ],
  "comment": "18 pages",
  "journal": "J. Differential Equations 239 (2007)251-271",
  "doi": "10.1016/j.jde.2007.03.029",
  "categories": [
    "math.AP"
  ],
  "abstract": "We first give the local well-posedness of strong solutions to the Cauchy problem of the 3D two-fluid MHD equations, then study the blow-up criterion of the strong solutions. By means of the Fourier frequency localization and Bony's paraproduct decomposition, it is proved that strong solution $(u,b)$ can be extended after $t=T$ if either $u\\in L^q_T(\\dot B^{0}_{p,\\infty})$ with $\\frac{2}{q}+\\frac{3}{p}\\le 1$ and $b\\in L^1_T(\\dot B^{0}_{\\infty,\\infty})$, or $(\\omega, J)\\in L^q_T(\\dot B^{0}_{p,\\infty})$ with $\\frac{2}{q}+\\frac{3}{p}\\le 2$, where $\\omega(t)=\\na\\times u $ denotes the vorticity of the velocity and $J=\\na\\times b$ the current density.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2007-03-13T12:20:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "76W05"
    ],
    "keywords": [
      "strong solution",
      "blow-up criterion",
      "existence theorem",
      "3d two-fluid mhd equations",
      "fourier frequency localization"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}