{
  "id": "math/0502104",
  "version": "v1",
  "published": "2005-02-05T01:44:57.000Z",
  "updated": "2005-02-05T01:44:57.000Z",
  "title": "On the local Smoothness of Solutions of the Navier-Stokes Equations",
  "authors": [
    "Hongjie Dong",
    "Dapeng Du"
  ],
  "comment": "14 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the Cauchy problem for incompressible Navier-Stokes equations $u_t+u\\nabla_xu-\\Delta u+\\nabla p=0, div u=0 in R^d \\times R^+$ with initial data $a\\in L^d(R^d)$, and study in some detail the smoothing effect of the equation. We prove that for $T<\\infty$ and for any positive integers $n$ and $m$ we have $t^{m+n/2}D^m_tD^{n}_x u\\in L^{d+2}(R^d\\times (0,T))$, as long as the $\\|u\\|_{L^{d+2}_{x,t}(R^d\\times (0,T))}$ stays finite.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-02-05T01:44:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D03",
      "76D05"
    ],
    "keywords": [
      "local smoothness",
      "cauchy problem",
      "initial data",
      "stays finite",
      "incompressible navier-stokes equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2104D"
    }
  }
}