[{"scopus_import":"1","OA_place":"repository","type":"journal_article","language":[{"iso":"eng"}],"publication":"American Journal of Mathematics","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"22057","page":"1-60","oa_version":"Preprint","publication_status":"published","month":"02","volume":129,"OA_type":"green","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.math/0501462"}],"status":"public","date_updated":"2026-06-29T10:30:01Z","doi":"10.1353/ajm.2007.0004","issue":"1","article_type":"original","arxiv":1,"author":[{"last_name":"Ryckman","full_name":"Ryckman, E","first_name":"E"},{"id":"056daca0-b8d1-11f0-964f-f91054abf8ca","last_name":"Visan","full_name":"Visan, Monica","first_name":"Monica"}],"oa":1,"date_published":"2007-02-01T00:00:00Z","day":"01","abstract":[{"lang":"eng","text":" We obtain global well-posedness, scattering, uniform regularity, and global L6t,x spacetime bounds for energy-space solutions to the defocusing energy-critical nonlinear Schrödinger equation in ℝ×ℝ4. Our arguments closely follow those of Colliander, Keel, et al., though our derivation of the frequency-localized interaction Morawetz estimate is somewhat simpler. As a consequence, our method yields a better bound on the L6t,x-norm. "}],"publisher":"Johns Hopkins University Press","article_processing_charge":"No","extern":"1","citation":{"short":"E. Ryckman, M. Vişan, American Journal of Mathematics 129 (2007) 1–60.","mla":"Ryckman, E., and Monica Vişan. “Global Well-Posedness and Scattering for the Defocusing Energy-Critical Nonlinear Schrödinger Equation in R 1+4.” <i>American Journal of Mathematics</i>, vol. 129, no. 1, Johns Hopkins University Press, 2007, pp. 1–60, doi:<a href=\"https://doi.org/10.1353/ajm.2007.0004\">10.1353/ajm.2007.0004</a>.","ama":"Ryckman E, Vişan M. Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4. <i>American Journal of Mathematics</i>. 2007;129(1):1-60. doi:<a href=\"https://doi.org/10.1353/ajm.2007.0004\">10.1353/ajm.2007.0004</a>","ieee":"E. Ryckman and M. Vişan, “Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4,” <i>American Journal of Mathematics</i>, vol. 129, no. 1. Johns Hopkins University Press, pp. 1–60, 2007.","ista":"Ryckman E, Vişan M. 2007. Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4. American Journal of Mathematics. 129(1), 1–60.","chicago":"Ryckman, E, and Monica Vişan. “Global Well-Posedness and Scattering for the Defocusing Energy-Critical Nonlinear Schrödinger Equation in R 1+4.” <i>American Journal of Mathematics</i>. Johns Hopkins University Press, 2007. <a href=\"https://doi.org/10.1353/ajm.2007.0004\">https://doi.org/10.1353/ajm.2007.0004</a>.","apa":"Ryckman, E., &#38; Vişan, M. (2007). Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4. <i>American Journal of Mathematics</i>. Johns Hopkins University Press. <a href=\"https://doi.org/10.1353/ajm.2007.0004\">https://doi.org/10.1353/ajm.2007.0004</a>"},"external_id":{"arxiv":["math/0501462"]},"publication_identifier":{"eissn":["1080-6377"]},"date_created":"2026-06-19T07:57:32Z","year":"2007","intvolume":"       129","das_tickbox":"1","title":"Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equation in R 1+4"}]