[{"arxiv":1,"OA_place":"repository","scopus_import":"1","quality_controlled":"1","doi":"10.1080/03605300903328109","author":[{"last_name":"Killip","first_name":"Rowan","full_name":"Killip, Rowan"},{"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"}],"_id":"22058","article_type":"original","date_created":"2026-06-19T07:57:55Z","mathsc":["35Q55","35B33"],"publication_status":"published","issue":"12","oa":1,"type":"journal_article","volume":34,"date_updated":"2026-06-29T10:20:21Z","status":"public","oa_version":"Preprint","publication":"Communications in Partial Differential Equations","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"11","publication_identifier":{"issn":["0360-5302","1532-4133"]},"extern":"1","das_tickbox":"1","language":[{"iso":"eng"}],"page":"1531-1565","date_published":"2009-11-01T00:00:00Z","abstract":[{"text":"We consider the defocusing H˙ 1-critical nonlinear Schr¨odinger equation in all dimensions (n ≥ 3) with a quadratic potential V (x) = ± 1/2|x|^2. We show global well-posedness for radial initial data obeying ∇u0(x), xu0(x) ∈L^2. In view of the potential V , this is the natural energy space. In the repulsive case, we also prove scattering. We follow the approach pioneered by Bourgain and Tao in the case of no potential; indeed, we include a proof of their results that incorporates a\r\ncouple of simplifications discovered while treating the problem with quadratic potential.","lang":"eng"}],"year":"2009","citation":{"short":"R. Killip, M. Vişan, X. Zhang, Communications in Partial Differential Equations 34 (2009) 1531–1565.","ieee":"R. Killip, M. Vişan, and X. Zhang, “Energy-critical NLS with quadratic potentials,” <i>Communications in Partial Differential Equations</i>, vol. 34, no. 12. Informa UK Limited, pp. 1531–1565, 2009.","apa":"Killip, R., Vişan, M., &#38; Zhang, X. (2009). Energy-critical NLS with quadratic potentials. <i>Communications in Partial Differential Equations</i>. Informa UK Limited. <a href=\"https://doi.org/10.1080/03605300903328109\">https://doi.org/10.1080/03605300903328109</a>","mla":"Killip, Rowan, et al. “Energy-Critical NLS with Quadratic Potentials.” <i>Communications in Partial Differential Equations</i>, vol. 34, no. 12, Informa UK Limited, 2009, pp. 1531–65, doi:<a href=\"https://doi.org/10.1080/03605300903328109\">10.1080/03605300903328109</a>.","ista":"Killip R, Vişan M, Zhang X. 2009. Energy-critical NLS with quadratic potentials. Communications in Partial Differential Equations. 34(12), 1531–1565.","ama":"Killip R, Vişan M, Zhang X. Energy-critical NLS with quadratic potentials. <i>Communications in Partial Differential Equations</i>. 2009;34(12):1531-1565. doi:<a href=\"https://doi.org/10.1080/03605300903328109\">10.1080/03605300903328109</a>","chicago":"Killip, Rowan, Monica Vişan, and Xiaoyi Zhang. “Energy-Critical NLS with Quadratic Potentials.” <i>Communications in Partial Differential Equations</i>. Informa UK Limited, 2009. <a href=\"https://doi.org/10.1080/03605300903328109\">https://doi.org/10.1080/03605300903328109</a>."},"intvolume":"        34","publisher":"Informa UK Limited","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.math/0611394","open_access":"1"}],"article_processing_charge":"No","OA_type":"green","title":"Energy-critical NLS with quadratic potentials","day":"01","external_id":{"arxiv":["math/0611394"]}}]