{
  "id": "2311.10006",
  "version": "v1",
  "published": "2023-11-16T16:40:21.000Z",
  "updated": "2023-11-16T16:40:21.000Z",
  "title": "Dean-Kawasaki equation with initial condition in the space of positive distributions",
  "authors": [
    "Vitalii Konarovskyi",
    "Fenna Müller"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that the Dean--Kawasaki equation does not admit nontrivial solutions in the space of tempered measures. More specifically, we consider martingale solutions taking values, and with initial conditions, in the subspace of measures admitting infinite mass and satisfying some integrability conditions. Following work by the first author, Lehmann and von Renesse [arXiv:1806.05018], we show that the equation only admits solutions if the initial measure is a discrete measure. Our result extends the previously mentioned works by allowing measures with infinite mass.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-16T16:40:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G57",
      "60H15",
      "60K35"
    ],
    "keywords": [
      "initial condition",
      "dean-kawasaki equation",
      "positive distributions",
      "measures admitting infinite mass",
      "admit nontrivial solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}