---
OA_place: repository
OA_type: green
_id: '22057'
abstract:
- lang: eng
  text: " We obtain global well-posedness, scattering, uniform regularity, and global
    L6t,x spacetime bounds for energy-space solutions to the defocusing energy-critical
    nonlinear Schrödinger equation in â\x84\x9DÃ\x97â\x84\x9D4. Our arguments closely
    follow those of Colliander, Keel, et al., though our derivation of the frequency-localized
    interaction Morawetz estimate is somewhat simpler. As a consequence, our method
    yields a better bound on the L6t,x-norm. "
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: E
  full_name: Ryckman, E
  last_name: Ryckman
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
citation:
  ama: Ryckman E, Vişan M. Global well-posedness and scattering for the defocusing
    energy-critical nonlinear Schrödinger equation in R 1+4. <i>American Journal of
    Mathematics</i>. 2007;129(1):1-60. doi:<a href="https://doi.org/10.1353/ajm.2007.0004">10.1353/ajm.2007.0004</a>
  apa: Ryckman, E., &#38; Vişan, M. (2007). Global well-posedness and scattering for
    the defocusing energy-critical nonlinear Schrödinger equation in R 1+4. <i>American
    Journal of Mathematics</i>. Johns Hopkins University Press. <a href="https://doi.org/10.1353/ajm.2007.0004">https://doi.org/10.1353/ajm.2007.0004</a>
  chicago: Ryckman, E, and Monica Vişan. “Global Well-Posedness and Scattering for
    the Defocusing Energy-Critical Nonlinear Schrödinger Equation in R 1+4.” <i>American
    Journal of Mathematics</i>. Johns Hopkins University Press, 2007. <a href="https://doi.org/10.1353/ajm.2007.0004">https://doi.org/10.1353/ajm.2007.0004</a>.
  ieee: E. Ryckman and M. Vişan, “Global well-posedness and scattering for the defocusing
    energy-critical nonlinear Schrödinger equation in R 1+4,” <i>American Journal
    of Mathematics</i>, vol. 129, no. 1. Johns Hopkins University Press, pp. 1–60,
    2007.
  ista: Ryckman E, Vişan M. 2007. Global well-posedness and scattering for the defocusing
    energy-critical nonlinear Schrödinger equation in R 1+4. American Journal of Mathematics.
    129(1), 1–60.
  mla: Ryckman, E., and Monica Vişan. “Global Well-Posedness and Scattering for the
    Defocusing Energy-Critical Nonlinear Schrödinger Equation in R 1+4.” <i>American
    Journal of Mathematics</i>, vol. 129, no. 1, Johns Hopkins University Press, 2007,
    pp. 1–60, doi:<a href="https://doi.org/10.1353/ajm.2007.0004">10.1353/ajm.2007.0004</a>.
  short: E. Ryckman, M. Vişan, American Journal of Mathematics 129 (2007) 1–60.
das_tickbox: '1'
date_created: 2026-06-19T07:57:32Z
date_published: 2007-02-01T00:00:00Z
date_updated: 2026-06-29T10:30:01Z
day: '01'
doi: 10.1353/ajm.2007.0004
extern: '1'
external_id:
  arxiv:
  - math/0501462
intvolume: '       129'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.math/0501462
month: '02'
oa: 1
oa_version: Preprint
page: 1-60
publication: American Journal of Mathematics
publication_identifier:
  eissn:
  - 1080-6377
publication_status: published
publisher: Johns Hopkins University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Global well-posedness and scattering for the defocusing energy-critical nonlinear
  Schrödinger equation in R 1+4
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 129
year: '2007'
...