{
  "id": "1805.03845",
  "version": "v1",
  "published": "2018-05-10T06:44:13.000Z",
  "updated": "2018-05-10T06:44:13.000Z",
  "title": "A Liouville type theorem for axially symmetric $D$-solutions to steady Navier-Stokes Equations",
  "authors": [
    "Na Zhao"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study axially symmetric $D$-solutions of three dimensional steady Navier-Stokes equations. We prove that if the velocity $u$ decays like $|x'|^{-(\\frac{2}{3})^+}$ uniformly for $z$, or the vorticity $\\omega$ decays like $|x'|^{-(\\frac{5}{3})^+}$ uniformly for $z$, then $u$ vanishes. Here $|x'|$ denotes the distance to the axis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-10T06:44:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "liouville type theorem",
      "dimensional steady navier-stokes equations",
      "study axially symmetric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}