{
  "id": "1512.01638",
  "version": "v1",
  "published": "2015-12-05T08:17:42.000Z",
  "updated": "2015-12-05T08:17:42.000Z",
  "title": "Landau equation for very soft and Coulomb potentials near Maxwellians",
  "authors": [
    "Kleber Carrapatoso",
    "Stéphane Mischler"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This work deals with the Landau equation for very soft and Coulomb potentials near the associated Maxwellian equilibrium. We first investigate the corresponding linearized operator and develop a method to prove stability estimates of its associated semigroup in large functional spaces. We then deduce existence, uniqueness and fast decay of the solutions to the nonlinear equation in a close-to-equilibrium framework. Our result drastically improves the set of initial data compared to the one considered by Guo and Strain who established similar results in [21, 37, 38]. Our functional framework is compatible with the non perturbative frameworks developed by Villani, Desvillettes and co-authors [42, 17, 16, 13], and our main result then makes possible to improve the speed of convergence to the equilibrium established therein.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-05T08:17:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "coulomb potentials",
      "landau equation",
      "large functional spaces",
      "associated maxwellian equilibrium",
      "deduce existence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}