{
  "id": "1507.01075",
  "version": "v1",
  "published": "2015-07-04T06:49:13.000Z",
  "updated": "2015-07-04T06:49:13.000Z",
  "title": "Determining modes for the surface Quasi-Geostrophic equation",
  "authors": [
    "Alexey Cheskidov",
    "Mimi Dai"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We introduce a determining wavenumber for the surface quasi-geostrophic (SQG) equation defined for each individual trajectory and then study its dependence on the force. While in the subcritical and critical cases this wavenumber has a uniform upper bound, it may blow up when the equation is supercritical. A bound on the determining wavenumber provides determining modes, which in some sense measure the number of degrees of freedom of the flow, or resolution needed to describe a solution to the SQG equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-04T06:49:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "37L30"
    ],
    "keywords": [
      "surface quasi-geostrophic equation",
      "determining modes",
      "determining wavenumber",
      "uniform upper bound",
      "sense measure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150701075C"
    }
  }
}