{
  "titles": [
    {
      "title": "Rough solutions for the periodic Korteweg-de Vries equation"
    }
  ],
  "creators": [
    {
      "name": "Gubinelli, M.",
      "nameType": "Personal",
      "familyName": "Gubinelli",
      "givenName": "M."
    }
  ],
  "publisher": {
    "name": "Papers of Massimiliano Gubinelli"
  },
  "publicationYear": 2006,
  "types": {
    "resourceTypeGeneral": "Preprint"
  },
  "version": "3",
  "url": "https://arxiv.org/abs/math/0610006v3",
  "dates": [
    {
      "date": "2006-09-30",
      "dateType": "Issued"
    },
    {
      "date": "2009-07-20",
      "dateType": "Available"
    },
    {
      "date": "2026-11-14",
      "dateType": "Updated"
    }
  ],
  "language": "en",
  "formats": [
    "application/pdf",
    "application/x-tex"
  ],
  "subjects": [
    {
      "subject": "math.AP",
      "subjectScheme": "arXiv"
    },
    {
      "subject": "math-ph",
      "subjectScheme": "arXiv"
    },
    {
      "subject": "math.MP",
      "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 show how to apply ideas from the theory of rough paths to the analysis of low-regularity solutions to non-linear dispersive equations. Our basic example will be the one dimensional Korteweg–de Vries (KdV) equation on a periodic domain and with initial condition in ${\\mathcal{F}} L^{\\alpha,p}$ spaces. We discuss convergence of Galerkin approximations, a modified Euler scheme and the presence of a random force of white-noise type in time.",
      "descriptionType": "Abstract"
    }
  ],
  "relatedIdentifiers": [
    {
      "relatedIdentifier": "arXiv:math/0610006v3",
      "relatedIdentifierType": "arXiv",
      "relationType": "IsIdenticalTo"
    },
    {
      "relatedIdentifier": "10.48550/arXiv.math/0610006",
      "relatedIdentifierType": "DOI",
      "relationType": "IsVersionOf"
    }
  ]
}