{
  "titles": [
    {
      "title": "Well-posedness of the transport equation by stochastic perturbation"
    }
  ],
  "creators": [
    {
      "name": "Flandoli, Franco",
      "nameType": "Personal",
      "familyName": "Flandoli",
      "givenName": "Franco"
    },
    {
      "name": "Gubinelli, Massimiliano",
      "nameType": "Personal",
      "familyName": "Gubinelli",
      "givenName": "Massimiliano"
    },
    {
      "name": "Priola, Enrico",
      "nameType": "Personal",
      "familyName": "Priola",
      "givenName": "Enrico"
    }
  ],
  "publisher": {
    "name": "Papers of Massimiliano Gubinelli"
  },
  "publicationYear": 2008,
  "types": {
    "resourceTypeGeneral": "Preprint"
  },
  "version": "2",
  "url": "https://arxiv.org/abs/0809.1310v2",
  "dates": [
    {
      "date": "2008-09-08",
      "dateType": "Issued"
    },
    {
      "date": "2009-05-08",
      "dateType": "Available"
    }
  ],
  "language": "en",
  "formats": [
    "application/pdf",
    "application/x-tex"
  ],
  "subjects": [
    {
      "subject": "math.AP",
      "subjectScheme": "arXiv"
    },
    {
      "subject": "math.PR",
      "subjectScheme": "arXiv"
    }
  ],
  "rightsList": [
    {
      "rights": "arXiv.org perpetual, non-exclusive license to distribute; all other rights reserved to the authors",
      "rightsUri": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
    }
  ],
  "descriptions": [
    {
      "description": "We consider the linear transport equation with a globally Holder continuous and bounded vector field. While this deterministic PDE may not be well-posed, we prove that a multiplicative stochastic perturbation of Brownian type is enough to render the equation well-posed. This seems to be the first explicit example of partial differential equation that become well-posed under the influece of noise. The key tool is a differentiable stochastic flow constructed and analysed by means of a special transformation of the drift of Ito-Tanaka type.",
      "descriptionType": "Abstract"
    }
  ],
  "relatedIdentifiers": [
    {
      "relatedIdentifier": "arXiv:0809.1310v2",
      "relatedIdentifierType": "arXiv",
      "relationType": "IsIdenticalTo"
    },
    {
      "relatedIdentifier": "10.48550/arXiv.0809.1310",
      "relatedIdentifierType": "DOI",
      "relationType": "IsVersionOf"
    },
    {
      "relatedIdentifier": "10.1007/s00222-009-0224-4",
      "relatedIdentifierType": "DOI",
      "relationType": "IsPreprintOf"
    }
  ]
}