{
  "id": "1403.1668",
  "version": "v2",
  "published": "2014-03-07T07:03:21.000Z",
  "updated": "2014-04-18T06:18:17.000Z",
  "title": "Landau damping in Sobolev spaces for the Vlasov-HMF model",
  "authors": [
    "Erwan Faou",
    "Frédéric Rousset"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the Vlasov-HMF (Hamiltonian Mean-Field) model. We consider solutions starting in a small Sobolev neighborhood of a spatially homogeneous state satisfying a linearized stability criterion (Penrose criterion). We prove that these solutions exhibit a scattering behavior to a modified state, which implies a nonlinear Landau damping effect with polynomial rate of damping.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-18T06:18:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "sobolev spaces",
      "vlasov-hmf model",
      "small sobolev neighborhood",
      "nonlinear landau damping effect",
      "linearized stability criterion"
    ],
    "publication": {
      "doi": "10.1007/s00205-015-0911-9",
      "journal": "Archive for Rational Mechanics and Analysis",
      "year": 2016,
      "month": "Feb",
      "volume": 219,
      "number": 2,
      "pages": 887
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016ArRMA.219..887F"
    }
  }
}