{
  "id": "2109.08598",
  "version": "v1",
  "published": "2021-09-17T15:21:17.000Z",
  "updated": "2021-09-17T15:21:17.000Z",
  "title": "Analysis and mean-field derivation of a porous-medium equation with fractional diffusion",
  "authors": [
    "Li Chen",
    "Alexandra Holzinger",
    "Ansgar Jüngel",
    "Nicola Zamponi"
  ],
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "A mean-field-type limit from stochastic moderately interacting many-particle systems with singular Riesz potential is performed, leading to nonlocal porous-medium equations in the whole space. The nonlocality is given by the inverse of a fractional Laplacian, and the limit equation can be interpreted as a transport equation with a fractional pressure. The proof is based on Oelschl\\\"ager's approach and a priori estimates for the associated diffusion equations, coming from energy-type and entropy inequalities as well as parabolic regularity. An existence analysis of the fractional porous-medium equation is also provided, based on a careful regularization procedure, new variants of fractional Gagliardo--Nirenberg inequalities, and the div-curl lemma. A consequence of the mean-field limit estimates is the propagation of chaos property.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-17T15:21:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K65",
      "35R11",
      "60H10",
      "60H30"
    ],
    "keywords": [
      "fractional diffusion",
      "mean-field derivation",
      "stochastic moderately interacting many-particle systems",
      "singular riesz potential",
      "fractional gagliardo-nirenberg inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}