{
  "id": "math/0703830",
  "version": "v2",
  "published": "2007-03-28T04:51:50.000Z",
  "updated": "2007-05-02T01:18:06.000Z",
  "title": "Nonexistence of self-similar singularities in the viscous magnetohydrodynamics with zero resistivity",
  "authors": [
    "Dongho Chae"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We are concerned on the possibility of finite time singularity in a partially viscous magnetohydrodynamic equations in $\\Bbb R^n$, $n=2,3$, namely the MHD with positive viscosity and zero resistivity. In the special case of zero magnetic field the system reduces to the Navier-Stokes equations in $\\Bbb R^n$. In this paper we exclude the scenario of finite time singularity in the form of self-similarity, under suitable integrability conditions on the velocity and the magnetic field. We also prove the nonexistence of asymptotically self-similar singularity. This provides us information on the behavior of solutions near possible singularity of general type as described in Corollary 1.1 below.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-05-02T01:18:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "zero resistivity",
      "finite time singularity",
      "nonexistence",
      "zero magnetic field",
      "viscous magnetohydrodynamic equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3830C"
    }
  }
}