{
  "id": "2007.16025",
  "version": "v1",
  "published": "2020-07-31T12:38:22.000Z",
  "updated": "2020-07-31T12:38:22.000Z",
  "title": "Mean-field limits: from particle descriptions to macroscopic equations",
  "authors": [
    "José A. Carrillo",
    "Young-Pil Choi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment interactions. We crucially make use of a discrete version of a modulated kinetic energy together with the bounded Lipschitz distance for measures in order to control terms in its time derivative due to the nonlocal interactions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-31T12:38:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "macroscopic equations",
      "mean-field limits",
      "derive pressureless euler-type equations",
      "nonlocal velocity fields",
      "newton-type particle descriptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}