{
  "id": "1407.5740",
  "version": "v2",
  "published": "2014-07-22T05:56:46.000Z",
  "updated": "2015-02-20T17:09:05.000Z",
  "title": "Self-similar Singularity of a 1D Model for the 3D Axisymmetric Euler Equations",
  "authors": [
    "Thomas Y. Hou",
    "Pengfei Liu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate the self-similar singularity of a 1D model for the 3D axisymmetric Euler equations, which is motivated by a particular singularity formation scenario observed in numerical computation. We prove the existence of a discrete family of self-similar profiles for this model and analyze their far-field properties. The self-similar profiles we find agree with direct simulation of the model and seem to have some stability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-22T05:56:46.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-20T17:09:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35"
    ],
    "keywords": [
      "3d axisymmetric euler equations",
      "self-similar singularity",
      "1d model",
      "self-similar profiles",
      "singularity formation scenario"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.5740H"
    }
  }
}