{
  "id": "2102.10610",
  "version": "v1",
  "published": "2021-02-21T14:20:05.000Z",
  "updated": "2021-02-21T14:20:05.000Z",
  "title": "Stochastic transport equation with singular drift",
  "authors": [
    "Damir Kinzebulatov",
    "Yuliy A. Semenov",
    "Renming Song"
  ],
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We prove existence, uniqueness and Sobolev regularity of weak solution of the Cauchy problem of the stochastic transport equation with drift in a large class of singular vector fields containing, in particular, the $L^d$ class, the weak $L^d$ class, as well as some vector fields that are not even in $L_{\\rm loc}^{2+\\varepsilon}$ for any $\\varepsilon>0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-21T14:20:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R60",
      "35A21"
    ],
    "keywords": [
      "stochastic transport equation",
      "singular drift",
      "sobolev regularity",
      "singular vector fields containing",
      "cauchy problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}