{
  "id": "1708.09648",
  "version": "v1",
  "published": "2017-08-31T10:09:29.000Z",
  "updated": "2017-08-31T10:09:29.000Z",
  "title": "Further remarks on the Luo-Hou's ansatz for a self-similar solution to the 3D Euler equations",
  "authors": [
    "Gianmarco Sperone"
  ],
  "comment": "For the moment, published online in \"Journal of Nonlinear Science\" (Sperone, G. J Nonlinear Sci (2017). https://doi.org/10.1007/s00332-017-9363-8)",
  "doi": "10.1007/s00332-017-9363-8",
  "categories": [
    "math.AP",
    "physics.flu-dyn"
  ],
  "abstract": "It is shown that the self-similar ansatz proposed by T. Hou and G. Luo to describe a singular solution of the 3D axisymmetric Euler equations leads, without assuming any asymptotic condition on the self-similar profiles, to an over-determined system of partial differential equations that produces two families of solutions: a class of trivial solutions in which the vorticity field is identically zero, and a family of solutions that blow-up immediately, where the vorticity field is governed by a stationary regime. In any case, the analytical properties of these solutions are not consistent with the numerical observations reported by T. Hou and G. Luo. Therefore, this result is a refinement of the previous work published by D. Chae and T.-P. Tsai on this matter, where the authors found the trivial class of solutions under a certain decay condition of the blow-up profiles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-31T10:09:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35C06",
      "35Q31",
      "76B03"
    ],
    "keywords": [
      "3d euler equations",
      "self-similar solution",
      "luo-hous ansatz",
      "vorticity field",
      "3d axisymmetric euler equations"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}