{
  "id": "1909.09960",
  "version": "v1",
  "published": "2019-09-22T08:01:40.000Z",
  "updated": "2019-09-22T08:01:40.000Z",
  "title": "New regularity criteria based on pressure or gradient of velocity in Lorentz spaces for the 3D Navier-Stokes equations",
  "authors": [
    "Xiang Ji",
    "Yanqing Wang",
    "Wei Wei"
  ],
  "comment": "10 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we derive regular criteria via pressure or gradient of the velocity in Lorentz spaces to the 3D Navier-Stokes equations. It is shown that a Leray-Hopf weak solution is regular on $(0,T]$ provided that either the norm $\\|\\Pi\\|_{L^{p,\\infty}(0,T; L ^{q,\\infty}(\\mathbb{R}^{3}))} $ with $ {2}/{p}+{3}/{q}=2$ $({3}/{2}<q<\\infty)$ or $\\|\\nabla\\Pi\\|_{L^{p,\\infty}(0,T; L ^{q,\\infty}(\\mathbb{R}^{3}))} $ with $ {2}/{p}+{3}/{q}=3$ $(1<q<\\infty)$ is small. This gives an affirmative answer to a question proposed by Suzuki in [26, Remark 2.4, p.3850]. Moreover, regular conditions in terms of $\\nabla u$ obtained here generalize known ones to allow the time direction to belong to Lorentz spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-22T08:01:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "3d navier-stokes equations",
      "lorentz spaces",
      "regularity criteria",
      "leray-hopf weak solution",
      "derive regular criteria"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}