[{"year":"2011","month":"05","mathsc":["35L71"],"date_published":"2011-05-01T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1002.1756","open_access":"1"}],"_id":"22061","quality_controlled":"1","language":[{"iso":"eng"}],"date_updated":"2026-06-29T10:44:15Z","volume":139,"title":"The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions","status":"public","page":"1805-1817","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2026-06-19T08:11:09Z","publisher":"American Mathematical Society","article_type":"original","publication_status":"published","publication":"Proceedings of the American Mathematical Society","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"}],"doi":"10.1090/s0002-9939-2010-10615-9","extern":"1","publication_identifier":{"eissn":["1088-6826"],"issn":["0002-9939"]},"oa_version":"Preprint","issue":"5","author":[{"first_name":"Rowan","last_name":"Killip","full_name":"Killip, Rowan"},{"first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","full_name":"Visan, Monica","last_name":"Visan"}],"OA_type":"green","external_id":{"arxiv":["1002.1756"]},"scopus_import":"1","intvolume":"       139","das_tickbox":"1","OA_place":"repository","day":"01","citation":{"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>","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>.","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.","short":"R. Killip, M. Vişan, Proceedings of the American Mathematical Society 139 (2011) 1805–1817.","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>","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>."},"oa":1,"article_processing_charge":"No","type":"journal_article"}]