{
  "id": "0708.3067",
  "version": "v2",
  "published": "2007-08-22T18:15:53.000Z",
  "updated": "2007-09-06T20:31:06.000Z",
  "title": "On the regularity of weak solutions of the 3D Navier-Stokes equations in $B^{-1}_{\\infty,\\infty}$",
  "authors": [
    "Alexey Cheskidov",
    "Roman Shvydkoy"
  ],
  "comment": "updated version -- a reference was added and a bug fixed",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that if a Leray-Hopf solution $u$ to the 3D Navier-Stokes equation belongs to $C((0,T]; B^{-1}_{\\infty,\\infty})$ or its jumps in the $B^{-1}_{\\infty,\\infty}$-norm do not exceed a constant multiple of viscosity, then $u$ is regular on $(0,T]$. Our method uses frequency local estimates on the nonlinear term, and yields an extension of the classical Ladyzhenskaya-Prodi-Serrin criterion.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-09-06T20:31:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76D03",
      "35Q30"
    ],
    "keywords": [
      "weak solutions",
      "3d navier-stokes equation belongs",
      "regularity",
      "frequency local estimates",
      "constant multiple"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.3067C"
    }
  }
}