{
  "id": "1703.08714",
  "version": "v1",
  "published": "2017-03-25T17:08:50.000Z",
  "updated": "2017-03-25T17:08:50.000Z",
  "title": "On critical spaces for the Navier-Stokes equations",
  "authors": [
    "Jan Pruess",
    "Mathias Wilke"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The abstract theory of critical spaces developed in [22] and [20] is applied to the Navier-Stokes equations in bounded domains with Navier boundary conditions as well as no-slip conditions. Our approach unifies, simplifies and extends existing work in the $L_p$-$L_q$ setting, considerably. As an essential step, it is shown that the strong and weak Stokes operators with Navier conditions admit an $\\mathcal{H}^\\infty$-calculus with $\\mathcal{H}^\\infty$-angle 0, and the real and complex interpolation spaces of these operators are identified.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-25T17:08:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "navier-stokes equations",
      "critical spaces",
      "navier conditions admit",
      "navier boundary conditions",
      "weak stokes operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}