---
OA_place: repository
OA_type: green
_id: '22029'
abstract:
- lang: eng
  text: We consider two classes of defocusing energy-supercritical nonlinear Schrödinger
    equations in dimensions d ≥ 5. We prove that if the solution u is a priori bounded
    in the critical Sobolev space, that is, {mathematical formular} , then u is global
    and scatters.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
  full_name: Killip, Rowan
  last_name: Killip
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
citation:
  ama: 'Killip R, Vişan M. Energy-supercritical NLS: Critical [Hdot]^s-bounds imply
    scattering. <i>Communications in Partial Differential Equations</i>. 2010;35(6):945-987.
    doi:<a href="https://doi.org/10.1080/03605301003717084">10.1080/03605301003717084</a>'
  apa: 'Killip, R., &#38; Vişan, M. (2010). Energy-supercritical NLS: Critical [Hdot]^s-bounds
    imply scattering. <i>Communications in Partial Differential Equations</i>. Informa
    UK Limited. <a href="https://doi.org/10.1080/03605301003717084">https://doi.org/10.1080/03605301003717084</a>'
  chicago: 'Killip, Rowan, and Monica Vişan. “Energy-Supercritical NLS: Critical [Hdot]^s-Bounds
    Imply Scattering.” <i>Communications in Partial Differential Equations</i>. Informa
    UK Limited, 2010. <a href="https://doi.org/10.1080/03605301003717084">https://doi.org/10.1080/03605301003717084</a>.'
  ieee: 'R. Killip and M. Vişan, “Energy-supercritical NLS: Critical [Hdot]^s-bounds
    imply scattering,” <i>Communications in Partial Differential Equations</i>, vol.
    35, no. 6. Informa UK Limited, pp. 945–987, 2010.'
  ista: 'Killip R, Vişan M. 2010. Energy-supercritical NLS: Critical [Hdot]^s-bounds
    imply scattering. Communications in Partial Differential Equations. 35(6), 945–987.'
  mla: 'Killip, Rowan, and Monica Vişan. “Energy-Supercritical NLS: Critical [Hdot]^s-Bounds
    Imply Scattering.” <i>Communications in Partial Differential Equations</i>, vol.
    35, no. 6, Informa UK Limited, 2010, pp. 945–87, doi:<a href="https://doi.org/10.1080/03605301003717084">10.1080/03605301003717084</a>.'
  short: R. Killip, M. Vişan, Communications in Partial Differential Equations 35
    (2010) 945–987.
date_created: 2026-06-19T07:41:22Z
date_published: 2010-06-01T00:00:00Z
date_updated: 2026-06-29T06:32:07Z
day: '01'
doi: 10.1080/03605301003717084
extern: '1'
external_id:
  arxiv:
  - '0812.2084'
intvolume: '        35'
issue: '6'
keyword:
- critical regularity
- Nonlinear Schrödinger equations
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.0812.2084
month: '06'
oa: 1
oa_version: Preprint
page: 945-987
publication: Communications in Partial Differential Equations
publication_identifier:
  eissn:
  - 1532-4133
  issn:
  - 0360-5302
publication_status: published
publisher: Informa UK Limited
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Energy-supercritical NLS: Critical [Hdot]^s-bounds imply scattering'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 35
year: '2010'
...