{"das_tickbox":"1","oa_version":"Preprint","oa":1,"article_type":"original","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.0804.1124"}],"OA_type":"green","month":"01","date_updated":"2026-06-30T11:48:07Z","abstract":[{"text":"Let 𝑑 ≥4 and let u be a global solution to the focusing mass-critical nonlinear Schrödinger equation 𝑖⁢𝑢𝑡 +Δ⁢𝑢 =−|𝑢|4𝑑 ⁢𝑢 with spherically symmetric 𝐻1𝑥 initial data and mass equal to that of the ground state Q. We prove that if u does not scatter, then, up to phase rotation and scaling, u is the solitary wave 𝑒𝑖⁢𝑡⁢𝑄. Combining this result with that of Merle [Duke Math. J., 69 (1993), pp. 427–453], we obtain that in dimensions 𝑑 ≥4, the only spherically symmetric minimal-mass nonscattering solutions are, up to phase rotation and scaling, the pseudoconformal ground state and the ground state solitary wave.","lang":"eng"}],"article_processing_charge":"No","doi":"10.1137/080720358","day":"01","extern":"1","publication_status":"published","_id":"22078","author":[{"first_name":"Rowan","full_name":"Killip, Rowan","last_name":"Killip"},{"last_name":"Li","full_name":"Li, Dong","first_name":"Dong"},{"last_name":"Visan","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","full_name":"Visan, Monica","first_name":"Monica"},{"full_name":"Zhang, Xiaoyi","first_name":"Xiaoyi","last_name":"Zhang"}],"external_id":{"arxiv":["0804.1124"]},"publisher":"Society for Industrial & Applied Mathematics","OA_place":"repository","publication_identifier":{"issn":["0036-1410"],"eissn":["1095-7154"]},"mathsc":["35Q55"],"date_published":"2009-01-01T00:00:00Z","arxiv":1,"page":"219-236","intvolume":"        41","title":"Characterization of minimal-mass blowup solutions to the focusing mass-critical NLS","publication":"SIAM Journal on Mathematical Analysis","language":[{"iso":"eng"}],"year":"2009","type":"journal_article","issue":"1","volume":41,"status":"public","citation":{"mla":"Killip, Rowan, et al. “Characterization of Minimal-Mass Blowup Solutions to the Focusing Mass-Critical NLS.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 41, no. 1, Society for Industrial &#38; Applied Mathematics, 2009, pp. 219–36, doi:<a href=\"https://doi.org/10.1137/080720358\">10.1137/080720358</a>.","ama":"Killip R, Li D, Vişan M, Zhang X. Characterization of minimal-mass blowup solutions to the focusing mass-critical NLS. <i>SIAM Journal on Mathematical Analysis</i>. 2009;41(1):219-236. doi:<a href=\"https://doi.org/10.1137/080720358\">10.1137/080720358</a>","short":"R. Killip, D. Li, M. Vişan, X. Zhang, SIAM Journal on Mathematical Analysis 41 (2009) 219–236.","ista":"Killip R, Li D, Vişan M, Zhang X. 2009. Characterization of minimal-mass blowup solutions to the focusing mass-critical NLS. SIAM Journal on Mathematical Analysis. 41(1), 219–236.","chicago":"Killip, Rowan, Dong Li, Monica Vişan, and Xiaoyi Zhang. “Characterization of Minimal-Mass Blowup Solutions to the Focusing Mass-Critical NLS.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial &#38; Applied Mathematics, 2009. <a href=\"https://doi.org/10.1137/080720358\">https://doi.org/10.1137/080720358</a>.","apa":"Killip, R., Li, D., Vişan, M., &#38; Zhang, X. (2009). Characterization of minimal-mass blowup solutions to the focusing mass-critical NLS. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial &#38; Applied Mathematics. <a href=\"https://doi.org/10.1137/080720358\">https://doi.org/10.1137/080720358</a>","ieee":"R. Killip, D. Li, M. Vişan, and X. Zhang, “Characterization of minimal-mass blowup solutions to the focusing mass-critical NLS,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 41, no. 1. Society for Industrial &#38; Applied Mathematics, pp. 219–236, 2009."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","quality_controlled":"1","date_created":"2026-06-19T08:25:50Z"}