---
OA_place: repository
OA_type: green
_id: '22061'
abstract:
- lang: eng
  text: "We consider the defocusing nonlinear wave equation utt − Δu +\r\n|u|\r\npu
    = 0 with spherically-symmetric initial data in the regime 4\r\nd−2 <p< 4\r\nd−3\r\n(which
    is energy-supercritical) and dimensions 3 ≤ d ≤ 6; we also consider\r\nd ≥ 7,
    but for a smaller range of p> 4\r\nd−2 . The principal result is that\r\nblowup
    (or failure to scatter) must be accompanied by blowup of the critical\r\nSobolev
    norm. An equivalent formulation is that maximal-lifespan solutions\r\nwith bounded
    critical Sobolev norm are global and scatter"
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. The radial defocusing energy-supercritical nonlinear wave
    equation in all space dimensions. <i>Proceedings of the American Mathematical
    Society</i>. 2011;139(5):1805-1817. doi:<a href="https://doi.org/10.1090/s0002-9939-2010-10615-9">10.1090/s0002-9939-2010-10615-9</a>
  apa: Killip, R., &#38; Vişan, M. (2011). The radial defocusing energy-supercritical
    nonlinear wave equation in all space dimensions. <i>Proceedings of the American
    Mathematical Society</i>. American Mathematical Society. <a href="https://doi.org/10.1090/s0002-9939-2010-10615-9">https://doi.org/10.1090/s0002-9939-2010-10615-9</a>
  chicago: Killip, Rowan, and Monica Vişan. “The Radial Defocusing Energy-Supercritical
    Nonlinear Wave Equation in All Space Dimensions.” <i>Proceedings of the American
    Mathematical Society</i>. American Mathematical Society, 2011. <a href="https://doi.org/10.1090/s0002-9939-2010-10615-9">https://doi.org/10.1090/s0002-9939-2010-10615-9</a>.
  ieee: R. Killip and M. Vişan, “The radial defocusing energy-supercritical nonlinear
    wave equation in all space dimensions,” <i>Proceedings of the American Mathematical
    Society</i>, vol. 139, no. 5. American Mathematical Society, pp. 1805–1817, 2011.
  ista: Killip R, Vişan M. 2011. The radial defocusing energy-supercritical nonlinear
    wave equation in all space dimensions. Proceedings of the American Mathematical
    Society. 139(5), 1805–1817.
  mla: Killip, Rowan, and Monica Vişan. “The Radial Defocusing Energy-Supercritical
    Nonlinear Wave Equation in All Space Dimensions.” <i>Proceedings of the American
    Mathematical Society</i>, vol. 139, no. 5, American Mathematical Society, 2011,
    pp. 1805–17, doi:<a href="https://doi.org/10.1090/s0002-9939-2010-10615-9">10.1090/s0002-9939-2010-10615-9</a>.
  short: R. Killip, M. Vişan, Proceedings of the American Mathematical Society 139
    (2011) 1805–1817.
das_tickbox: '1'
date_created: 2026-06-19T08:11:09Z
date_published: 2011-05-01T00:00:00Z
date_updated: 2026-06-29T10:44:15Z
day: '01'
doi: 10.1090/s0002-9939-2010-10615-9
extern: '1'
external_id:
  arxiv:
  - '1002.1756'
intvolume: '       139'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1002.1756
mathsc:
- 35L71
month: '05'
oa: 1
oa_version: Preprint
page: 1805-1817
publication: Proceedings of the American Mathematical Society
publication_identifier:
  eissn:
  - 1088-6826
  issn:
  - 0002-9939
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: The radial defocusing energy-supercritical nonlinear wave equation in all space
  dimensions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 139
year: '2011'
...