{
  "id": "0912.1316",
  "version": "v2",
  "published": "2009-12-07T19:22:19.000Z",
  "updated": "2012-02-28T02:08:00.000Z",
  "title": "On Singularity Formation of a 3D Model for Incompressible Navier-Stokes Equations",
  "authors": [
    "Thomas Y. Hou",
    "Zuoqiang Shi",
    "Shu Wang"
  ],
  "comment": "33 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate the singularity formation of a 3D model that was recently proposed by Hou and Lei in [16] for axisymmetric 3D incompressible Navier-Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier-Stokes equations is that the convection term is neglected in the 3D model. This model shares many properties of the 3D incompressible Navier-Stokes equations. One of the main results of this paper is that we prove rigorously the finite time singularity formation of the 3D inviscid model for a class of initial boundary value problems with smooth initial data of finite energy. We also prove the global regularity of the 3D inviscid model for a class of small smooth initial data.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-02-28T02:08:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "3d model",
      "3d inviscid model",
      "axisymmetric 3d incompressible navier-stokes equations",
      "small smooth initial data",
      "finite time singularity formation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.1316H"
    }
  }
}