{
  "id": "math/0209323",
  "version": "v1",
  "published": "2002-09-24T12:35:44.000Z",
  "updated": "2002-09-24T12:35:44.000Z",
  "title": "A sufficient condition for a finite-time $ L_2 $ singularity of the 3d Euler Equation",
  "authors": [
    "Xinyu He"
  ],
  "comment": "AMS_Tex, 8 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "A sufficient condition is derived for a finite-time $L_2$ singularity of the 3d incompressible Euler equations, making appropriate assumptions on eigenvalues of the Hessian of pressure. Under this condition $\\lim_{t \\to T_*} \\sup | \\frac{D \\o} {Dt} |_{L_2(\\vO)} = \\infty$, where $~ \\vO \\subset \\R3$ moves with the fluid. In particular, $|{\\o}|$, $|\\S_{ij}| , and $|\\P_{ij}|$ all become unbounded at one point $(x_1,T_1)$, $T_1$ being the first blow-up time in $L_2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-09-24T12:35:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76B03",
      "76D05"
    ],
    "keywords": [
      "3d euler equation",
      "sufficient condition",
      "singularity",
      "finite-time",
      "3d incompressible euler equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......9323H"
    }
  }
}