{
  "id": "0906.5140",
  "version": "v1",
  "published": "2009-06-28T15:07:54.000Z",
  "updated": "2009-06-28T15:07:54.000Z",
  "title": "Well-posedness for fractional Navier-Stokes equations in critical spaces close to $\\dot{B}^{-(2β-1)}_{\\infty,\\infty}(\\mathbb{R}^{n})$",
  "authors": [
    "Zhichun Zhai"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we prove the well-posedness for the fractional Navier-Stokes equations in critical spaces $G^{-(2\\beta-1)}_{n}(\\mathbb{R}^{n})$ and $BMO^{-(2\\beta-1)}(\\mathbb{R}^{n}).$ Both of them are close to the largest critical space $\\dot{B}^{-(2\\beta-1)}_{\\infty,\\infty}(\\mathbb{R}^{n}).$ In $G^{-(2\\beta-1)}_{n}(\\mathbb{R}^{n}),$ we establish the well-posedness based on a priori estimates for the fractional Navier-Stokes equations in Besov spaces. To obtain the well-posedness in $BMO^{-(2\\beta-1)}(\\mathbb{R}^{n}),$ we find a relationship between $Q_{\\alpha;\\infty}^{\\beta,-1}(\\mathbb{R}^{n})$ and $BMO(\\mathbb{R}^{n})$ by giving an equivalent characterization of $BMO^{-\\zeta}(\\mathbb{R}^{n}).$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-06-28T15:07:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D03",
      "42B35",
      "46E30"
    ],
    "keywords": [
      "fractional navier-stokes equations",
      "critical spaces close",
      "well-posedness",
      "largest critical space",
      "priori estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.5140Z"
    }
  }
}