---
OA_place: repository
OA_type: green
_id: '22075'
abstract:
- lang: eng
  text: 'In this short note, we present a new proof of the global well-posedness and
    scattering result for the defocusing energy-critical nonlinear Schrödinger equation
    (NLS) in four space dimensions obtained previously by Ryckman and Visan [“Global
    well-posedness and scattering for the defocusing energycritical nonlinear Schrödinger
    equation in R^1+4⁠.” American Journal of Mathematics 129 (2007): 1–60. MR2288737].
    The argument is inspired by the recent work of Dodson [“Global well-posedness
    and scattering for the defocusing, L2-critical, nonlinear Schrödinger equation
    when d≥3.” (2009): preprint arXiv:0912.2467.] on the mass-critical NLS.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
citation:
  ama: Vişan M. Global well-posedness and scattering for the defocusing cubic nonlinear
    Schrödinger equation in four dimensions. <i>International Mathematics Research
    Notices</i>. 2012;2012(5):1037-1067. doi:<a href="https://doi.org/10.1093/imrn/rnr051">10.1093/imrn/rnr051</a>
  apa: Vişan, M. (2012). Global well-posedness and scattering for the defocusing cubic
    nonlinear Schrödinger equation in four dimensions. <i>International Mathematics
    Research Notices</i>. Oxford University Press. <a href="https://doi.org/10.1093/imrn/rnr051">https://doi.org/10.1093/imrn/rnr051</a>
  chicago: Vişan, Monica. “Global Well-Posedness and Scattering for the Defocusing
    Cubic Nonlinear Schrödinger Equation in Four Dimensions.” <i>International Mathematics
    Research Notices</i>. Oxford University Press, 2012. <a href="https://doi.org/10.1093/imrn/rnr051">https://doi.org/10.1093/imrn/rnr051</a>.
  ieee: M. Vişan, “Global well-posedness and scattering for the defocusing cubic nonlinear
    Schrödinger equation in four dimensions,” <i>International Mathematics Research
    Notices</i>, vol. 2012, no. 5. Oxford University Press, pp. 1037–1067, 2012.
  ista: Vişan M. 2012. Global well-posedness and scattering for the defocusing cubic
    nonlinear Schrödinger equation in four dimensions. International Mathematics Research
    Notices. 2012(5), 1037–1067.
  mla: Vişan, Monica. “Global Well-Posedness and Scattering for the Defocusing Cubic
    Nonlinear Schrödinger Equation in Four Dimensions.” <i>International Mathematics
    Research Notices</i>, vol. 2012, no. 5, Oxford University Press, 2012, pp. 1037–67,
    doi:<a href="https://doi.org/10.1093/imrn/rnr051">10.1093/imrn/rnr051</a>.
  short: M. Vişan, International Mathematics Research Notices 2012 (2012) 1037–1067.
das_tickbox: '1'
date_created: 2026-06-19T08:23:13Z
date_published: 2012-05-01T00:00:00Z
date_updated: 2026-06-30T11:21:51Z
day: '01'
doi: 10.1093/imrn/rnr051
extern: '1'
external_id:
  arxiv:
  - '1011.1526'
intvolume: '      2012'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1011.1526
month: '05'
oa: 1
oa_version: Preprint
page: 1037-1067
publication: International Mathematics Research Notices
publication_identifier:
  eissn:
  - 1687-0247
  issn:
  - 1073-7928
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Global well-posedness and scattering for the defocusing cubic nonlinear Schrödinger
  equation in four dimensions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2012
year: '2012'
...