[{"date_created":"2026-06-19T08:23:13Z","scopus_import":"1","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Vişan, Monica. “Global Well-Posedness and Scattering for the Defocusing Cubic Nonlinear Schrödinger Equation in Four Dimensions.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2012. <a href=\"https://doi.org/10.1093/imrn/rnr051\">https://doi.org/10.1093/imrn/rnr051</a>.","apa":"Vişan, M. (2012). Global well-posedness and scattering for the defocusing cubic nonlinear Schrödinger equation in four dimensions. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnr051\">https://doi.org/10.1093/imrn/rnr051</a>","ieee":"M. Vişan, “Global well-posedness and scattering for the defocusing cubic nonlinear Schrödinger equation in four dimensions,” <i>International Mathematics Research Notices</i>, vol. 2012, no. 5. Oxford University Press, pp. 1037–1067, 2012.","mla":"Vişan, Monica. “Global Well-Posedness and Scattering for the Defocusing Cubic Nonlinear Schrödinger Equation in Four Dimensions.” <i>International Mathematics Research Notices</i>, vol. 2012, no. 5, Oxford University Press, 2012, pp. 1037–67, doi:<a href=\"https://doi.org/10.1093/imrn/rnr051\">10.1093/imrn/rnr051</a>.","ama":"Vişan M. Global well-posedness and scattering for the defocusing cubic nonlinear Schrödinger equation in four dimensions. <i>International Mathematics Research Notices</i>. 2012;2012(5):1037-1067. doi:<a href=\"https://doi.org/10.1093/imrn/rnr051\">10.1093/imrn/rnr051</a>","short":"M. Vişan, International Mathematics Research Notices 2012 (2012) 1037–1067.","ista":"Vişan M. 2012. Global well-posedness and scattering for the defocusing cubic nonlinear Schrödinger equation in four dimensions. International Mathematics Research Notices. 2012(5), 1037–1067."},"volume":2012,"status":"public","type":"journal_article","year":"2012","issue":"5","language":[{"iso":"eng"}],"title":"Global well-posedness and scattering for the defocusing cubic nonlinear Schrödinger equation in four dimensions","publication":"International Mathematics Research Notices","intvolume":"      2012","page":"1037-1067","arxiv":1,"date_published":"2012-05-01T00:00:00Z","publication_identifier":{"eissn":["1687-0247"],"issn":["1073-7928"]},"OA_place":"repository","extern":"1","publication_status":"published","_id":"22075","external_id":{"arxiv":["1011.1526"]},"publisher":"Oxford University Press","author":[{"first_name":"Monica","full_name":"Visan, Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","last_name":"Visan"}],"day":"01","abstract":[{"lang":"eng","text":"In this short note, we present a new proof of the global well-posedness and scattering result for the defocusing energy-critical nonlinear Schrödinger equation (NLS) in four space dimensions obtained previously by Ryckman and Visan [“Global well-posedness and scattering for the defocusing energycritical nonlinear Schrödinger equation in R^1+4⁠.” American Journal of Mathematics 129 (2007): 1–60. MR2288737]. The argument is inspired by the recent work of Dodson [“Global well-posedness and scattering for the defocusing, L2-critical, nonlinear Schrödinger equation when d≥3.” (2009): preprint arXiv:0912.2467.] on the mass-critical NLS."}],"article_processing_charge":"No","doi":"10.1093/imrn/rnr051","date_updated":"2026-06-30T11:21:51Z","month":"05","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1011.1526"}],"OA_type":"green","article_type":"original","oa":1,"das_tickbox":"1","oa_version":"Preprint"}]