{
  "id": "2303.02281",
  "version": "v2",
  "published": "2023-03-04T00:52:35.000Z",
  "updated": "2023-05-30T17:10:41.000Z",
  "title": "Nonlinear regularization estimates and global well-posedness for the Landau-Coulomb equation near equilibrium",
  "authors": [
    "William Golding",
    "Maria Gualdani",
    "Amélie Loher"
  ],
  "comment": "25 pages; minor revisions to introduction and changes to the title/abstract",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the Landau equation with Coulomb potential in the spatially homogeneous case. We show short time propagation of smallness in $L^p$ norms for $p>3/2$ and instantaneous regularization in Sobolev spaces. This yields new short time quantitative a priori estimates that are unconditional near equilibrium. We combine these estimates with existing literature on global well-posedness for regular data to extend the well-posedness theory to small $L^p$ data with $p$ arbitrarily close to $3/2$. The threshold $p = 3/2$ agrees with previous work on conditional regularity for the Landau equation in the far from equilibrium regime.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2023-05-30T17:10:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q82",
      "82B40",
      "35A01",
      "35A02",
      "35B65"
    ],
    "keywords": [
      "nonlinear regularization estimates",
      "global well-posedness",
      "landau-coulomb equation",
      "landau equation",
      "short time propagation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}