{
  "id": "math/0703095",
  "version": "v1",
  "published": "2007-03-03T18:27:03.000Z",
  "updated": "2007-03-03T18:27:03.000Z",
  "title": "Decay Asymptotics of the Viscous Camassa-Holm Equations in the Plane",
  "authors": [
    "Clayton Bjorland"
  ],
  "comment": "22 pages, submitted",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the vorticity formulation of the 2-D viscous Camassa-Holm equations in the whole space. We establish global existence for solutions corresponding to initial data in $L^1$ and describe the large time behavior of solutions with sufficiently small and localized initial data. We calculate the rate at which such solutions approach an ``un-filtered'' Oseen vortex by computing the rate at which the solution of a scaled vorticity problem approaches the solution to a corresponding linearized equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-03-03T18:27:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40",
      "35K55"
    ],
    "keywords": [
      "viscous camassa-holm equations",
      "decay asymptotics",
      "large time behavior",
      "scaled vorticity problem approaches",
      "localized initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......3095B"
    }
  }
}