{
  "id": "0711.1113",
  "version": "v3",
  "published": "2007-11-07T16:44:07.000Z",
  "updated": "2007-11-20T16:16:54.000Z",
  "title": "On the blow-up problem and new a priori estimates for the 3D Euler and the Navier-Stokes equations",
  "authors": [
    "Dongho Chae"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study blow-up rates and the blow-up profiles of possible asymptotically self-similar singularities of the 3D Euler equations, where the sense of convergence and self-similarity are considered in various sense. We extend much further, in particular, the previous nonexistence results of self-similar/asymptotically self-similar singularities obtained in \\cite{cha1,cha2}. Some implications the notions for the 3D Navier-Stokes equations are also deduced. Generalization of the self-similar transforms is also considered, and by appropriate choice of the transform we obtain new \\textit{a priori} estimates for the 3D Euler and the Navier-Stokes equations.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-11-20T16:16:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76B03",
      "76D05"
    ],
    "keywords": [
      "blow-up problem",
      "priori estimates",
      "3d navier-stokes equations",
      "3d euler equations",
      "study blow-up rates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0711.1113C"
    }
  }
}