{
  "id": "1310.8307",
  "version": "v5",
  "published": "2013-10-30T20:06:27.000Z",
  "updated": "2014-04-02T19:52:19.000Z",
  "title": "Regularity criteria in weak $L^3$ for 3D incompressible Navier-Stokes equations",
  "authors": [
    "Yuwen Luo",
    "Tai-Peng Tsai"
  ],
  "comment": "16 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the regularity of a distributional solution $(u,p)$ of the 3D incompressible evolution Navier-Stokes equations. Let $B_r$ denote concentric balls in $\\mathbb{R}^3$ with radius $r$. We will show that if $p\\in L^{m} (0,1; L^1(B_2))$, $m>2$, and if $u$ is sufficiently small in $L^{\\infty} (0,1; L^{3,\\infty}(B_2))$, without any assumption on its gradient, then $u$ is bounded in $B_1\\times (\\frac{1}{10},1)$. It is an endpoint case of the usual Serrin-type regularity criteria, and extends the steady-state result of Kim-Kozono to the time dependent setting. In the appendix we also show some nonendpoint borderline regularity criteria.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2014-04-02T19:52:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "3d incompressible navier-stokes equations",
      "nonendpoint borderline regularity criteria",
      "usual serrin-type regularity criteria",
      "3d incompressible evolution navier-stokes equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.8307L"
    }
  }
}