---
OA_place: repository
OA_type: green
_id: '22031'
abstract:
- lang: eng
  text: We analyze the blowup behaviour of solutions to the focusing nonlinear Klein–Gordon
    equation in spatial dimensions d>=2. We obtain upper bounds on the blowup rate,
    both globally in space and in light cones. The results are sharp in the conformal
    and sub-conformal cases. The argument relies on Lyapunov functionals derived from
    the dilation identity. We also prove that the critical Sobolev norm diverges near
    the blowup time.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Rowan
  full_name: Killip, Rowan
  last_name: Killip
- first_name: Betsy
  full_name: Stovall, Betsy
  last_name: Stovall
- first_name: Monica
  full_name: Visan, Monica
  id: 056daca0-b8d1-11f0-964f-f91054abf8ca
  last_name: Visan
citation:
  ama: Killip R, Stovall B, Vişan M. Blowup behaviour for the nonlinear Klein-Gordon
    equation. <i>Mathematische Annalen</i>. 2014;358(1-2):289-350. doi:<a href="https://doi.org/10.1007/s00208-013-0960-z">10.1007/s00208-013-0960-z</a>
  apa: Killip, R., Stovall, B., &#38; Vişan, M. (2014). Blowup behaviour for the nonlinear
    Klein-Gordon equation. <i>Mathematische Annalen</i>. Springer Nature. <a href="https://doi.org/10.1007/s00208-013-0960-z">https://doi.org/10.1007/s00208-013-0960-z</a>
  chicago: Killip, Rowan, Betsy Stovall, and Monica Vişan. “Blowup Behaviour for the
    Nonlinear Klein-Gordon Equation.” <i>Mathematische Annalen</i>. Springer Nature,
    2014. <a href="https://doi.org/10.1007/s00208-013-0960-z">https://doi.org/10.1007/s00208-013-0960-z</a>.
  ieee: R. Killip, B. Stovall, and M. Vişan, “Blowup behaviour for the nonlinear Klein-Gordon
    equation,” <i>Mathematische Annalen</i>, vol. 358, no. 1–2. Springer Nature, pp.
    289–350, 2014.
  ista: Killip R, Stovall B, Vişan M. 2014. Blowup behaviour for the nonlinear Klein-Gordon
    equation. Mathematische Annalen. 358(1–2), 289–350.
  mla: Killip, Rowan, et al. “Blowup Behaviour for the Nonlinear Klein-Gordon Equation.”
    <i>Mathematische Annalen</i>, vol. 358, no. 1–2, Springer Nature, 2014, pp. 289–350,
    doi:<a href="https://doi.org/10.1007/s00208-013-0960-z">10.1007/s00208-013-0960-z</a>.
  short: R. Killip, B. Stovall, M. Vişan, Mathematische Annalen 358 (2014) 289–350.
das_tickbox: '1'
date_created: 2026-06-19T07:42:09Z
date_published: 2014-02-01T00:00:00Z
date_updated: 2026-06-22T11:16:03Z
day: '01'
doi: 10.1007/s00208-013-0960-z
extern: '1'
external_id:
  arxiv:
  - '1203.4886'
intvolume: '       358'
issue: 1-2
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1203.4886
month: '02'
oa: 1
oa_version: Preprint
page: 289-350
publication: Mathematische Annalen
publication_identifier:
  eissn:
  - 1432-1807
  issn:
  - 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Blowup behaviour for the nonlinear Klein-Gordon equation
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 358
year: '2014'
...