{
  "id": "math/0410344",
  "version": "v1",
  "published": "2004-10-15T06:12:33.000Z",
  "updated": "2004-10-15T06:12:33.000Z",
  "title": "On the uniqueness of the solution of the two-dimensional Navier-Stokes equation with a Dirac mass as initial vorticity",
  "authors": [
    "Isabelle Gallagher",
    "Thierry Gallay",
    "Pierre-Louis Lions"
  ],
  "comment": "9 pages, no figure",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We propose two different proofs of the fact that Oseen's vortex is the unique solution of the two-dimensional Navier-Stokes equation with a Dirac mass as initial vorticity. The first argument, due to C.E. Wayne and the second author, is based on an entropy estimate for the vorticity equation in self-similar variables. The second proof is new and relies on symmetrization techniques for parabolic equations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-10-15T06:12:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "35A07",
      "76D05",
      "76D17"
    ],
    "keywords": [
      "two-dimensional navier-stokes equation",
      "dirac mass",
      "initial vorticity",
      "uniqueness",
      "symmetrization techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10344G"
    }
  }
}