{
  "id": "math/0701054",
  "version": "v1",
  "published": "2007-01-02T10:57:15.000Z",
  "updated": "2007-01-02T10:57:15.000Z",
  "title": "The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations",
  "authors": [
    "Qionglei Chen",
    "Changxing Miao",
    "Zhifei Zhang"
  ],
  "comment": "12pages",
  "journal": "Commun. Math. Phys. 275(2007)861-872",
  "doi": "10.1007/s00220-007-0319-y",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the blow-up criterion of smooth solutions to the 3D MHD equations. By means of the Littlewood-Paley decomposition, we prove a Beale-Kato-Majda type blow-up criterion of smooth solutions via the vorticity of velocity only, i. e. $\\sup_{j\\in\\Z}\\int_0^T\\|\\Delta_j(\\na\\times u)\\|_\\infty dt$, where $\\Delta_j$ is a frequency localization on $|\\xi|\\approx 2^j$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-02T10:57:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76W05",
      "35B65"
    ],
    "keywords": [
      "3d magneto-hydrodynamics equations",
      "beale-kato-majda criterion",
      "beale-kato-majda type blow-up criterion",
      "smooth solutions",
      "3d mhd equations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Commun. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}