[{"arxiv":1,"month":"12","scopus_import":"1","_id":"22090","OA_place":"repository","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","citation":{"short":"R. Killip, T. Tao, M. Vişan, Journal of the European Mathematical Society 11 (2009) 1203–1258.","mla":"Killip, Rowan, et al. “The Cubic Nonlinear Schrödinger Equation in Two Dimensions with Radial Data.” <i>Journal of the European Mathematical Society</i>, vol. 11, no. 6, European Mathematical Society Press, 2009, pp. 1203–58, doi:<a href=\"https://doi.org/10.4171/jems/180\">10.4171/jems/180</a>.","chicago":"Killip, Rowan, Terence Tao, and Monica Vişan. “The Cubic Nonlinear Schrödinger Equation in Two Dimensions with Radial Data.” <i>Journal of the European Mathematical Society</i>. European Mathematical Society Press, 2009. <a href=\"https://doi.org/10.4171/jems/180\">https://doi.org/10.4171/jems/180</a>.","ista":"Killip R, Tao T, Vişan M. 2009. The cubic nonlinear Schrödinger equation in two dimensions with radial data. Journal of the European Mathematical Society. 11(6), 1203–1258.","apa":"Killip, R., Tao, T., &#38; Vişan, M. (2009). The cubic nonlinear Schrödinger equation in two dimensions with radial data. <i>Journal of the European Mathematical Society</i>. European Mathematical Society Press. <a href=\"https://doi.org/10.4171/jems/180\">https://doi.org/10.4171/jems/180</a>","ama":"Killip R, Tao T, Vişan M. The cubic nonlinear Schrödinger equation in two dimensions with radial data. <i>Journal of the European Mathematical Society</i>. 2009;11(6):1203-1258. doi:<a href=\"https://doi.org/10.4171/jems/180\">10.4171/jems/180</a>","ieee":"R. Killip, T. Tao, and M. Vişan, “The cubic nonlinear Schrödinger equation in two dimensions with radial data,” <i>Journal of the European Mathematical Society</i>, vol. 11, no. 6. European Mathematical Society Press, pp. 1203–1258, 2009."},"volume":11,"type":"journal_article","oa":1,"doi":"10.4171/jems/180","publisher":"European Mathematical Society Press","language":[{"iso":"eng"}],"date_published":"2009-12-23T00:00:00Z","issue":"6","article_type":"original","extern":"1","external_id":{"arxiv":["0707.3188"]},"das_tickbox":"1","page":"1203-1258","quality_controlled":"1","year":"2009","title":"The cubic nonlinear Schrödinger equation in two dimensions with radial data","day":"23","OA_type":"green","author":[{"full_name":"Killip, Rowan","last_name":"Killip","first_name":"Rowan"},{"full_name":"Tao, Terence","last_name":"Tao","first_name":"Terence"},{"last_name":"Visan","full_name":"Visan, Monica","first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"}],"oa_version":"Preprint","intvolume":"        11","date_updated":"2026-07-01T12:57:57Z","abstract":[{"text":"We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation iu \r\nt\r\n​\r\n +Δu=±∣u∣ \r\n2\r\n u for large spherically symmetric L \r\nx\r\n2\r\n​\r\n (R \r\n2\r\n ) initial data; in the focusing case we require, of course, that the mass is strictly less than that of the ground state. As a consequence, we deduce that in the focusing case, any spherically symmetric blowup solution must concentrate at least the mass of the ground state at the blowup time.\r\n\r\nWe also establish some partial results towards the analogous claims in other dimensions and without the assumption of spherical symmetry.","lang":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.0707.3188"}],"date_created":"2026-06-19T08:49:58Z","status":"public","article_processing_charge":"No","publication_identifier":{"eissn":["1435-9863"],"issn":["1435-9855"]},"publication":"Journal of the European Mathematical Society"}]