{
  "id": "1603.06037",
  "version": "v1",
  "published": "2016-03-19T03:35:05.000Z",
  "updated": "2016-03-19T03:35:05.000Z",
  "title": "Global well-posedness of the Boltzmann equation with large amplitude initial data",
  "authors": [
    "Renjun Duan",
    "Feimin Huang",
    "Yong Wang",
    "Tong Yang"
  ],
  "comment": "34 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The global well-posedness of the Boltzmann equation with initial data of large amplitude has remained a long-standing open problem. In this paper, by developing a new $L^\\infty_xL^1_{v}\\cap L^\\infty_{x,v}$ approach, we prove the global existence and uniqueness of mild solutions to the Boltzmann equation in the whole space or torus for a class of initial data with bounded velocity-weighted $L^\\infty$ norm under some smallness condition on $L^1_xL^\\infty_v$ norm as well as defect mass, energy and entropy so that the initial data allow large amplitude oscillations. Both the hard and soft potentials with angular cut-off are considered, and the large time behavior of solutions in $L^\\infty_{x,v}$ norm with explicit rates of convergence is also studied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-19T03:35:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large amplitude initial data",
      "boltzmann equation",
      "global well-posedness",
      "large amplitude oscillations",
      "large time behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160306037D"
    }
  }
}