{"article_type":"original","issue":"2","doi":"10.2140/apde.2008.1.229","abstract":[{"text":"We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation (mathematical formular)  for large spherically symmetric L2/x(R^d) initial data in dimensions d >= 3.\r\nIn the focusing case we require that the mass is strictly less than that of the ground state. As a consequence, we obtain that in the focusing case, any spherically symmetric blowup solution must concentrate at least the mass of the ground state at the blowup time.","lang":"eng"}],"day":"01","date_published":"2008-06-01T00:00:00Z","arxiv":1,"author":[{"first_name":"Rowan","full_name":"Killip, Rowan","last_name":"Killip"},{"full_name":"Visan, Monica","first_name":"Monica","last_name":"Visan","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"},{"first_name":"Xiaoyi","full_name":"Zhang, Xiaoyi","last_name":"Zhang"}],"oa":1,"citation":{"ama":"Killip R, Vişan M, Zhang X. The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher. <i>Analysis &#38; PDE</i>. 2008;1(2):229-266. doi:<a href=\"https://doi.org/10.2140/apde.2008.1.229\">10.2140/apde.2008.1.229</a>","mla":"Killip, Rowan, et al. “The Mass-Critical Nonlinear Schrödinger Equation with Radial Data in Dimensions Three and Higher.” <i>Analysis &#38; PDE</i>, vol. 1, no. 2, Mathematical Sciences Publishers, 2008, pp. 229–66, doi:<a href=\"https://doi.org/10.2140/apde.2008.1.229\">10.2140/apde.2008.1.229</a>.","short":"R. Killip, M. Vişan, X. Zhang, Analysis &#38; PDE 1 (2008) 229–266.","apa":"Killip, R., Vişan, M., &#38; Zhang, X. (2008). The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher. <i>Analysis &#38; PDE</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/apde.2008.1.229\">https://doi.org/10.2140/apde.2008.1.229</a>","chicago":"Killip, Rowan, Monica Vişan, and Xiaoyi Zhang. “The Mass-Critical Nonlinear Schrödinger Equation with Radial Data in Dimensions Three and Higher.” <i>Analysis &#38; PDE</i>. Mathematical Sciences Publishers, 2008. <a href=\"https://doi.org/10.2140/apde.2008.1.229\">https://doi.org/10.2140/apde.2008.1.229</a>.","ista":"Killip R, Vişan M, Zhang X. 2008. The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher. Analysis &#38; PDE. 1(2), 229–266.","ieee":"R. Killip, M. Vişan, and X. Zhang, “The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher,” <i>Analysis &#38; PDE</i>, vol. 1, no. 2. Mathematical Sciences Publishers, pp. 229–266, 2008."},"extern":"1","article_processing_charge":"No","publisher":"Mathematical Sciences Publishers","das_tickbox":"1","title":"The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher","date_created":"2026-06-19T08:27:33Z","year":"2008","intvolume":"         1","external_id":{"arxiv":["0708.0849"]},"publication_identifier":{"issn":["2157-5045"],"eissn":["1948-206X"]},"OA_place":"repository","type":"journal_article","scopus_import":"1","publication":"Analysis & PDE","language":[{"iso":"eng"}],"_id":"22082","page":"229-266","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","quality_controlled":"1","status":"public","date_updated":"2026-07-01T07:15:15Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.0708.0849","open_access":"1"}],"OA_type":"green","month":"06","publication_status":"published","volume":1}