{
  "id": "2102.06152",
  "version": "v1",
  "published": "2021-02-11T17:51:54.000Z",
  "updated": "2021-02-11T17:51:54.000Z",
  "title": "An anisotropic regularity condition for the 3D incompressible Navier-Stokes equations for the entire exponent range",
  "authors": [
    "Igor Kukavica",
    "Wojciech S. Ożański"
  ],
  "comment": "9 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that a suitable weak solution to the incompressible Navier-Stokes equations on ${\\mathbb{R}^3\\times(-1,1)}$ is regular on $\\mathbb{R}^3\\times(0,1]$ if $\\partial_3 u $ belongs to a Morrey space $M^{2p/(2p-3),\\alpha } ((-1,0);L^p (\\mathbb{R}^3 ))$ for any $\\alpha >1$ and $p\\in (3/2,\\infty)$. For each $\\alpha >1$ the Morrey space is, up to a logarithm, critical with respect to the scaling of the equations, and contains all spaces $L^q ((-1,0);L^p (\\mathbb{R}^3 ))$ that are subcritical, that is for which $2/q+3/p<1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-11T17:51:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "3d incompressible navier-stokes equations",
      "anisotropic regularity condition",
      "entire exponent range",
      "morrey space",
      "weak solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}