{
  "id": "1203.5151",
  "version": "v2",
  "published": "2012-03-23T01:47:06.000Z",
  "updated": "2012-04-17T17:01:56.000Z",
  "title": "Finite Time Blow-up of a 3D Model for Incompressible Euler Equations",
  "authors": [
    "Thomas Y. Hou",
    "Zhen Lei"
  ],
  "comment": "This paper has been withdrawn by the author. We are not able to construct data which meets the requirements in the main Theorem at this moment",
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate the role of convection on its large time behavior of 3D incompressible Euler equations. In \\cite{HL09a}, we constructed a new 3D model by neglecting the convection term from the reformulated axisymmetric Navier-Stokes equations. This model preserves almost all the properties of the full Navier-Stokes equations, including an energy identity for smooth solutions. The numerical evidence presented in \\cite{HL09a} seems to support that the 3D model may develop a finite time singularity. In this paper, we prove rigorously that the 3D inviscid model develops a finite time singularity for a family of smooth initial data whose energy is finite and conserved in time.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-04-17T17:01:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "3d model",
      "finite time blow-up",
      "finite time singularity",
      "large time behavior",
      "full navier-stokes equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.5151H"
    }
  }
}