{
  "id": "1711.05072",
  "version": "v1",
  "published": "2017-11-14T12:10:07.000Z",
  "updated": "2017-11-14T12:10:07.000Z",
  "title": "Strong solution for stochastic transport equations with irregular drift: existence and non-existence",
  "authors": [
    "Jinlong Wei",
    "Jinqiao Duan",
    "Hongjun Gao",
    "Guangying Lv"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove some existence, uniqueness and non-existence results of stochastic strong solutions for a class of stochastic transport equations with a $q$-integrable (in time), bounded and $\\alpha$-H\\\"{o}lder continuous (in space) drift coefficient. More precisely, we show that for a Sobolev differentiable initial condition, there exists a unique stochastic strong solution when $\\alpha>2/q$, while for $\\alpha+1<2/q$ with spatial dimension higher than one, we can choose proper initial data and drift coefficients so that there is no stochastic strong solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-14T12:10:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35A01",
      "35L02"
    ],
    "keywords": [
      "stochastic transport equations",
      "irregular drift",
      "non-existence",
      "unique stochastic strong solution",
      "drift coefficient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}