---
res:
  bibo_abstract:
  - "We prove global well-posedness of the Korteweg–de Vries equation for\r\ninitial
    data in the space H^−1(R). This is sharp in the class of H^s(R) spaces.\r\nEven
    local well-posedness was previously unknown for s < −3/4. The proof\r\nis based
    on the introduction of a new method of general applicability for the\r\nstudy
    of low-regularity well-posedness for integrable PDE, informed by the\r\nexistence
    of commuting flows. In particular, as we will show, completely\r\nparallel arguments
    give a new proof of global well-posedness for KdV with\r\nperiodic H−1 data, shown
    previously by Kappeler and Topalov, as well as\r\nglobal well-posedness for the
    fifth order KdV equation in L^2(R).\r\nAdditionally, we give a new proof of the
    a priori local smoothing bound\r\nof Buckmaster and Koch for KdV on the line.
    Moreover, we upgrade this\r\nestimate to show that convergence of initial data
    in H^−1(R) guarantees\r\nconvergence of the resulting solutions in L^2loc(R ×
    R). Thus, solutions with\r\nH^−1(R) initial data are distributional solutions.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Rowan
      foaf_name: Killip, Rowan
      foaf_surname: Killip
  - foaf_Person:
      foaf_givenName: Monica
      foaf_name: Visan, Monica
      foaf_surname: Visan
      foaf_workInfoHomepage: http://www.librecat.org/personId=056daca0-b8d1-11f0-964f-f91054abf8ca
  bibo_doi: 10.4007/annals.2019.190.1.4
  bibo_issue: '1'
  bibo_volume: 190
  dct_date: 2019^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0003-486X
  dct_language: eng
  dct_publisher: Annals of Mathematics@
  dct_title: KdV is well-posed in H^-1@
...