[{"author":[{"full_name":"Killip, Rowan","first_name":"Rowan","last_name":"Killip"},{"full_name":"Stovall, Betsy","first_name":"Betsy","last_name":"Stovall"},{"last_name":"Visan","first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","full_name":"Visan, Monica"}],"das_tickbox":"1","external_id":{"arxiv":["1203.4886"]},"publication_status":"published","volume":358,"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."}],"month":"02","language":[{"iso":"eng"}],"oa":1,"issue":"1-2","intvolume":"       358","article_type":"original","year":"2014","date_published":"2014-02-01T00:00:00Z","date_created":"2026-06-19T07:42:09Z","type":"journal_article","extern":"1","arxiv":1,"article_processing_charge":"No","quality_controlled":"1","doi":"10.1007/s00208-013-0960-z","publication_identifier":{"eissn":["1432-1807"],"issn":["0025-5831"]},"status":"public","page":"289-350","oa_version":"Preprint","scopus_import":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2026-06-22T11:16:03Z","OA_type":"green","day":"01","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>","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.","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>.","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>","short":"R. Killip, B. Stovall, M. Vişan, Mathematische Annalen 358 (2014) 289–350.","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>.","ista":"Killip R, Stovall B, Vişan M. 2014. Blowup behaviour for the nonlinear Klein-Gordon equation. Mathematische Annalen. 358(1–2), 289–350."},"publication":"Mathematische Annalen","publisher":"Springer Nature","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1203.4886"}],"OA_place":"repository","title":"Blowup behaviour for the nonlinear Klein-Gordon equation","_id":"22031"}]