{
  "id": "1811.07797",
  "version": "v2",
  "published": "2018-11-19T16:52:09.000Z",
  "updated": "2019-10-13T17:07:47.000Z",
  "title": "On mean field limit for Brownian particles with Coulomb interaction in 3D",
  "authors": [
    "Lei Li",
    "Jian-Guo Liu",
    "Pu Yu"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "In this paper, we consider the mean field limit of Brownian particles with Coulomb interaction in 3D space. In particular, using a symmetrization technique, we show that the limit measure almost surely is a weak solution to the limiting nonlinear Fokker-Planck equation. By proving that the energy almost surely is bounded by the initial energy, we improve the regularity of the weak solutions. Moreover, by a natural assumption, we establish the weak strong uniqueness principle, which is closely related to the propagation of chaos.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2019-10-13T17:07:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q70",
      "60H10",
      "35Q84",
      "60G57"
    ],
    "keywords": [
      "mean field limit",
      "brownian particles",
      "coulomb interaction",
      "weak strong uniqueness principle",
      "weak solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}