{
  "id": "1603.00540",
  "version": "v1",
  "published": "2016-03-02T01:11:43.000Z",
  "updated": "2016-03-02T01:11:43.000Z",
  "title": "A gradient flow approach to the Boltzmann equation",
  "authors": [
    "Matthias Erbar"
  ],
  "comment": "30 pages, comments are welcome",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that the spatially homogeneous Boltzmann equation (with constant collision kernel) evolves as the gradient flow of the entropy with respect to a suitable geometry on the space of probability measures. This geometry is given by a new notion of distance between probability measures, which takes the collision process into account. As a first application, we obtain a novel time-discrete approximation scheme for the homogeneous Boltzmann equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-02T01:11:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gradient flow approach",
      "probability measures",
      "novel time-discrete approximation scheme",
      "constant collision kernel",
      "spatially homogeneous boltzmann equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}