{
  "id": "0909.3707",
  "version": "v1",
  "published": "2009-09-21T08:41:37.000Z",
  "updated": "2009-09-21T08:41:37.000Z",
  "title": "An H^1 setting for the Navier-Stokes equations: quantitative estimates",
  "authors": [
    "Carlo Morosi",
    "Livio Pizzocchero"
  ],
  "comment": "LaTeX; 33 pages",
  "journal": "Nonlinear Analysis: TMA 74(6) (2011), 2398-2414 (in a slightly revised version)",
  "doi": "10.1016/j.na.2010.11.043",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the incompressible Navier-Stokes (NS) equations on a torus, in the setting of the spaces L^2 and H^1; our approach is based on a general framework for semi- or quasi-linear parabolic equations proposed in the previous work [9]. We present some estimates on the linear semigroup generated by the Laplacian and on the quadratic NS nonlinearity; these are fully quantitative, i.e., all the constants appearing therein are given explicitly. As an application we show that, on a three dimensional torus T^3, the (mild) solution of the NS Cauchy problem is global for each H^1 initial datum u_0 with zero mean, such that || curl u_0 ||_{L^2} <= 0.407; this improves the bound for global existence || curl u_0 ||_{L^2} <= 0.00724, derived recently by Robinson and Sadowski [10]. We announce some future applications, based again on the H^1 framework and on the general scheme of [9].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-21T08:41:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D03",
      "76D05"
    ],
    "keywords": [
      "navier-stokes equations",
      "quantitative estimates",
      "quasi-linear parabolic equations",
      "ns cauchy problem",
      "quadratic ns nonlinearity"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.3707M"
    }
  }
}