{
  "id": "1508.03318",
  "version": "v1",
  "published": "2015-08-13T19:38:13.000Z",
  "updated": "2015-08-13T19:38:13.000Z",
  "title": "Regularity Criterion to the axially symmetric Navier-Stokes Equations",
  "authors": [
    "Dongyi Wei"
  ],
  "comment": "13 pages, 0 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "Smooth solutions to the axially symmetric Navier-Stokes equations obey the following maximum principle:$\\|ru_\\theta(r,z,t)\\|_{L^\\infty}\\leq\\|ru_\\theta(r,z,0)\\|_{L^\\infty}.$ We first prove the global regularity of solutions if $\\|ru_\\theta(r,z,0)\\|_{L^\\infty}$ or $ \\|ru_\\theta(r,z,t)\\|_{L^\\infty(r\\leq r_0)}$ is small compared with certain dimensionless quantity of the initial data. This result improves the one in Zhen Lei and Qi S. Zhang \\cite{1}. As a corollary, we also prove the global regularity under the assumption that $|ru_\\theta(r,z,t)|\\leq\\ |\\ln r|^{-3/2},\\ \\ \\forall\\ 0<r\\leq\\delta_0\\in(0,1/2).$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-13T19:38:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D05",
      "76D07",
      "76N10"
    ],
    "keywords": [
      "regularity criterion",
      "axially symmetric navier-stokes equations obey",
      "global regularity",
      "smooth solutions",
      "maximum principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150803318W"
    }
  }
}