{
  "titles": [
    {
      "title": "Paracontrolled approach to the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity"
    }
  ],
  "creators": [
    {
      "name": "Gubinelli, Massimiliano",
      "nameType": "Personal",
      "familyName": "Gubinelli",
      "givenName": "Massimiliano"
    },
    {
      "name": "Koch, Herbert",
      "nameType": "Personal",
      "familyName": "Koch",
      "givenName": "Herbert"
    },
    {
      "name": "Oh, Tadahiro",
      "nameType": "Personal",
      "familyName": "Oh",
      "givenName": "Tadahiro"
    }
  ],
  "publisher": {
    "name": "Papers of Massimiliano Gubinelli"
  },
  "publicationYear": 2018,
  "types": {
    "resourceTypeGeneral": "Preprint"
  },
  "version": "3",
  "url": "https://arxiv.org/abs/1811.07808v3",
  "dates": [
    {
      "date": "2018-11-19",
      "dateType": "Issued"
    },
    {
      "date": "2021-06-22",
      "dateType": "Available"
    },
    {
      "date": "2026-11-14",
      "dateType": "Updated"
    }
  ],
  "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": "Using ideas from paracontrolled calculus, we prove local well-posedness of a renormalized version of the three-dimensional stochastic nonlinear wave equation with quadratic nonlinearity forced by an additive space-time white noise on a periodic domain. There are two new ingredients as compared to the parabolic setting. (i) In constructing stochastic objects, we have to carefully exploit dispersion at a multilinear level. (ii) We introduce novel random operators and leverage their regularity to overcome the lack of smoothing of usual paradifferential commutators.",
      "descriptionType": "Abstract"
    }
  ],
  "relatedIdentifiers": [
    {
      "relatedIdentifier": "arXiv:1811.07808v3",
      "relatedIdentifierType": "arXiv",
      "relationType": "IsIdenticalTo"
    },
    {
      "relatedIdentifier": "10.48550/arXiv.1811.07808",
      "relatedIdentifierType": "DOI",
      "relationType": "IsVersionOf"
    }
  ]
}