{
  "id": "0903.1461",
  "version": "v2",
  "published": "2009-03-08T21:51:14.000Z",
  "updated": "2009-05-09T16:20:35.000Z",
  "title": "The Navier-Stokes equations in the critical Lebesgue space",
  "authors": [
    "Hongjie Dong",
    "Dapeng Du"
  ],
  "comment": "20 pages, to appear in Comm. Math. Phys",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study regularity criteria for the $d$-dimensional incompressible Navier-Stokes equations. We prove in this paper that if $u\\in L_\\infty^tL_{d}^x((0,T)\\times {\\mathbb R}^d)$ is a Leray-Hopf weak solution, then $u$ is smooth and unique in $(0,T)\\times \\bR^d$. This generalizes a result by Escauriaza, Seregin and \\v{S}ver\\'ak. Additionally, we show that if $T=\\infty$ then $u$ goes to zero as $t$ goes to infinity.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-05-09T16:20:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D03",
      "76D05"
    ],
    "keywords": [
      "critical lebesgue space",
      "dimensional incompressible navier-stokes equations",
      "leray-hopf weak solution",
      "study regularity criteria"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00220-009-0852-y",
      "journal": "Communications in Mathematical Physics",
      "year": 2009,
      "month": "Dec",
      "volume": 292,
      "number": 3,
      "pages": 811
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009CMaPh.292..811D"
    }
  }
}