{
  "id": "math/0601060",
  "version": "v2",
  "published": "2006-01-04T07:28:01.000Z",
  "updated": "2006-01-16T01:02:23.000Z",
  "title": "Nonexistence of self-similar singularities for the 3D incompressible Euler equations",
  "authors": [
    "Dongho Chae"
  ],
  "comment": "This version refines the previous one by relaxing the condition of compact support for the vorticity",
  "doi": "10.1007/s00220-007-0249-8",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove that there exists no self-similar finite time blowing up solution to the 3D incompressible Euler equations. By similar method we also show nonexistence of self-similar blowing up solutions to the divergence-free transport equation in $\\Bbb R^n$. This result has direct applications to the density dependent Euler equations, the Boussinesq system, and the quasi-geostrophic equations, for which we also show nonexistence of self-similar blowing up solutions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-01-16T01:02:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "3d incompressible euler equations",
      "self-similar singularities",
      "nonexistence",
      "density dependent euler equations",
      "divergence-free transport equation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer",
      "journal": "Commun. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}