{
  "titles": [
    {
      "title": "Regularization by noise and stochastic Burgers equations"
    }
  ],
  "creators": [
    {
      "name": "Gubinelli, M.",
      "nameType": "Personal",
      "familyName": "Gubinelli",
      "givenName": "M."
    },
    {
      "name": "Jara, M.",
      "nameType": "Personal",
      "familyName": "Jara",
      "givenName": "M."
    }
  ],
  "publisher": {
    "name": "Papers of Massimiliano Gubinelli"
  },
  "publicationYear": 2012,
  "types": {
    "resourceTypeGeneral": "Preprint"
  },
  "version": "2",
  "url": "https://arxiv.org/abs/1208.6551v2",
  "dates": [
    {
      "date": "2012-08-31",
      "dateType": "Issued"
    },
    {
      "date": "2013-04-09",
      "dateType": "Available"
    }
  ],
  "language": "en",
  "formats": [
    "application/pdf",
    "application/x-tex"
  ],
  "subjects": [
    {
      "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 study a generalized 1d periodic SPDE of Burgers type: $ \\partial_t u =- A^\\theta u + \\partial_x u^2 + A^{\\theta/2} \\xi $ where $\\theta > 1/2$, $-A$ is the 1d Laplacian, $\\xi$ is a space-time white noise and the initial condition $u_0$ is taken to be (space) white noise. We introduce a notion of weak solution for this equation in the stationary setting. For these solutions we point out how the noise provide a regularizing effect allowing to prove existence and suitable estimates when $\\theta>1/2$. When $\\theta>5/4$ we obtain pathwise uniqueness. We discuss the use of the same method to study different approximations of the same equation and for a model of stationary 2d stochastic Navier-Stokes evolution.",
      "descriptionType": "Abstract"
    }
  ],
  "relatedIdentifiers": [
    {
      "relatedIdentifier": "arXiv:1208.6551v2",
      "relatedIdentifierType": "arXiv",
      "relationType": "IsIdenticalTo"
    },
    {
      "relatedIdentifier": "10.48550/arXiv.1208.6551",
      "relatedIdentifierType": "DOI",
      "relationType": "IsVersionOf"
    }
  ]
}