{
  "id": "math/0608578",
  "version": "v1",
  "published": "2006-08-23T13:08:28.000Z",
  "updated": "2006-08-23T13:08:28.000Z",
  "title": "Affine Variant of Fractional Sobolev Space with Application to Navier-Stokes System",
  "authors": [
    "Jie Xiao"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "It is proved that for $\\alpha\\in (0,1)$, $Q_\\alpha(\\rn)$, not only as an intermediate space of $W^{1,n}(\\rn)$ and $BMO(\\rn)$ but also as an affine variant of Sobolev space $\\dot{L}^{2}_\\alpha(\\rn)$ which is sharply imbedded in $L^{\\frac{2n}{n-2\\alpha}}(\\rn)$, is isomorphic to a quadratic Morrey space under fractional differentiation. At the same time, the dot product $\\nabla\\cdot\\big(Q_\\alpha(\\rn)\\big)^n$ is applied to derive the well-posedness of the scaling invariant mild solutions of the incompressible Navier-Stokes system in $\\bn=(0,\\infty)\\times\\rn$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-08-23T13:08:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional sobolev space",
      "affine variant",
      "application",
      "quadratic morrey space",
      "scaling invariant mild solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8578X"
    }
  }
}