{
  "id": "0902.4247",
  "version": "v2",
  "published": "2009-02-24T21:35:31.000Z",
  "updated": "2009-10-15T12:57:04.000Z",
  "title": "On the rate of convergence of the two-dimensional $α$-models of turbulence to the Navier-Stokes equations",
  "authors": [
    "Y. Cao",
    "E. S. Titi"
  ],
  "comment": "29 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "Rates of convergence of solutions of various two-dimensional $\\alpha-$regularization models, subject to periodic boundary conditions, toward solutions of the exact Navier-Stokes equations are given in the $L^\\infty$-$L^2$ time-space norm, in terms of the regularization parameter $ \\alpha$, when $\\alpha$ approaches zero. Furthermore, as a paradigm, error estimates for the Galerkin approximation of the exact two-dimensional Leray-$\\alpha$ model are also presented in the $L^\\infty$-$L^2$ time-space norm. Simply by the triangle inequality, one can reach the error estimates of the solutions of Galerkin approximation of the $\\alpha$-regularization models toward the exact solutions of the Navier-Stokes equations in the two-dimensional periodic boundary conditions case.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-15T12:57:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A30",
      "35Q35",
      "65M12",
      "65M15",
      "76D05"
    ],
    "keywords": [
      "convergence",
      "two-dimensional periodic boundary conditions case",
      "regularization models",
      "time-space norm",
      "error estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.4247C"
    }
  }
}