---
res:
  bibo_abstract:
  - "We consider both the defocusing and focusing cubic nonlinear Klein–Gordon equations\r\nutt
    − Δu + u ± u3 =0\r\nin two space dimensions for real-valued initial data u(0)
    ∈ H1/x and ut(0) ∈ L2/x.\r\nWe show that in the defocusing case, solutions are
    global and have finite global L4/t,x spacetime bounds. In the focusing case, we
    characterize the dichotomy\r\nbetween this behaviour and blowup for initial data
    with energy less than that\r\nof the ground state.\r\nThese results rely on analogous
    statements for the two-dimensional cubic\r\nnonlinear Schr¨odinger equation, which
    are known in the defocusing case and\r\nfor spherically-symmetric initial data
    in the focusing case. Thus, our results\r\nare mostly unconditional.\r\nIt was
    previously shown by Nakanishi that spacetime bounds for Klein–\r\nGordon equations
    imply the same for nonlinear Schr¨odinger equations.@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Rowan
      foaf_name: Killip, Rowan
      foaf_surname: Killip
  - foaf_Person:
      foaf_givenName: Betsy
      foaf_name: Stovall, Betsy
      foaf_surname: Stovall
  - 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: 10.1090/s0002-9947-2011-05536-4
  bibo_issue: '3'
  bibo_volume: 364
  dct_date: 2012^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0002-9947
  - http://id.crossref.org/issn/1088-6850
  dct_language: eng
  dct_publisher: American Mathematical Society@
  dct_title: Scattering for the cubic Klein-Gordon equation in two space dimensions@
...