{
  "id": "2305.07626",
  "version": "v1",
  "published": "2023-05-12T17:26:55.000Z",
  "updated": "2023-05-12T17:26:55.000Z",
  "title": "Quantitative Estimates and Global Strong Solutions for the 1D Boltzmann Equation",
  "authors": [
    "Dominic Wynter"
  ],
  "comment": "28 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We prove quantitative growth estimates for large data solutions to the Boltzmann equation in one spatial dimension, for a collision kernel with angular cutoff. We prove in full the results presented in the note of Biryuk, Craig, and Panferov, and obtain improved bounds for large data. We show that solutions are unique, and propagate $W^{k,1}_\\ell$ norms by a Beale-Kato-Majda criterion. We obtain quantitative uniform bounds on the density $\\rho$ by $Ce^{C\\sqrt{t}}$ for initial data with small relative entropy, and by $Ce^{Ct}$ for general initial data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-12T17:26:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global strong solutions",
      "1d boltzmann equation",
      "quantitative estimates",
      "large data solutions",
      "general initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}