{
  "id": "1606.08126",
  "version": "v1",
  "published": "2016-06-27T05:18:22.000Z",
  "updated": "2016-06-27T05:18:22.000Z",
  "title": "On the Geometric Regularity Conditions for the 3D Navier-Stokes Equations",
  "authors": [
    "Dongho Chae",
    "Jihoon Lee"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $v$ and $\\omega$ be the velocity and the vorticity of a suitable weak solutions of the 3D Navier-Stokes equations in a space-time domain containing $z_0= (x_0, t_0)$, and let $Q_{z_0, r}=B_{x_0, r} \\times (t_0-r^2, t_0)$ be a parabolic cylinder in the domain. We show that if either $\\left(v \\times \\frac{\\omega}{|\\omega|}\\right) \\cdot \\frac{\\nabla \\times \\omega}{|\\nabla \\times \\omega|} \\in L^{\\gamma, \\alpha}_{x,t}(Q_{z_0, r})$ with $\\frac{3}{\\gamma}+\\frac{2}{\\alpha} \\leq 1$, or $\\left(\\omega \\times \\frac{v}{|v|}\\right) \\cdot \\frac{\\nabla \\times \\omega}{|\\nabla \\times \\omega|} \\in L^{\\gamma, \\alpha}_{x,t}(Q_{z_0, r})$ with $\\frac{3}{\\gamma}+\\frac{2}{\\alpha} \\leq 2$, ($\\gamma \\geq 2$, $\\alpha \\geq 2$), where $L^{\\gamma, \\alpha}_{x,t}$ denote the Serrin type of class, then $z_0$ is a regular point for $v$. This improves previous local regularity criteria for the suitable weak solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-27T05:18:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D03",
      "76D05"
    ],
    "keywords": [
      "3d navier-stokes equations",
      "geometric regularity conditions",
      "suitable weak solutions",
      "local regularity criteria",
      "parabolic cylinder"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}