{
  "id": "2008.10269",
  "version": "v1",
  "published": "2020-08-24T09:01:53.000Z",
  "updated": "2020-08-24T09:01:53.000Z",
  "title": "Global solutions in $W_k^{ζ,p}L^\\infty_TL^2_v$ for the Boltzmann equation without cutoff",
  "authors": [
    "Haoyu Zhang"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The Boltzmann equation without an angular cutoff in a three-dimensional periodic domain is considered. The global-in-time existence of solutions in a function space $ W_k^{\\zeta,p}L^\\infty_TL^2_v $ with $p>1$ and $\\zeta>3(1-\\frac{1}{p})$ is established in the perturbation framework and the long-time behavior of solutions is also obtained for both hard and soft potentials. The proof is based on several norm estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-24T09:01:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "boltzmann equation",
      "global solutions",
      "three-dimensional periodic domain",
      "global-in-time existence",
      "angular cutoff"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}