{
  "id": "2407.08670",
  "version": "v1",
  "published": "2024-07-11T16:59:57.000Z",
  "updated": "2024-07-11T16:59:57.000Z",
  "title": "A blow-down mechanism for the Landau-Coulomb equation",
  "authors": [
    "Maria Pia Gualdani",
    "Raphael Winter"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We investigate the Landau-Coulomb equation and show an explicit blow-down mechanism for a family of initial data that are small-scale, supercritical perturbations of a Maxwellian function. We establish global well-posedness and show that the initial bump region will disappear in a time of order one. We prove that the function remains close to an explicit function during the blow-down. As a consequence, our result shows exponential decay in time of the solution towards equilibrium. The key ingredients of our proof are the explicit blow-down function and a novel two-scale linearization in appropriate time-dependent spaces that yields uniform estimates in the perturbation parameter.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-11T16:59:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B25"
    ],
    "keywords": [
      "landau-coulomb equation",
      "yields uniform estimates",
      "explicit blow-down mechanism",
      "function remains close",
      "explicit blow-down function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}