[{"intvolume":"        30","date_created":"2026-06-19T08:47:48Z","year":"2017","publication_identifier":{"issn":["0893-4983"]},"external_id":{"arxiv":["1603.08912"]},"title":"The focusing cubic NLS with inverse-square potential in three space dimensions","das_tickbox":"1","citation":{"ista":"Killip R, Murphy J, Vişan M, Zheng J. 2017. The focusing cubic NLS with inverse-square potential in three space dimensions. Differential and Integral Equations. 30(3/4), 161–206.","ieee":"R. Killip, J. Murphy, M. Vişan, and J. Zheng, “The focusing cubic NLS with inverse-square potential in three space dimensions,” <i>Differential and Integral Equations</i>, vol. 30, no. 3/4. Khayyam Publishing, pp. 161–206, 2017.","chicago":"Killip, Rowan, Jason Murphy, Monica Vişan, and Jiqiang Zheng. “The Focusing Cubic NLS with Inverse-Square Potential in Three Space Dimensions.” <i>Differential and Integral Equations</i>. Khayyam Publishing, 2017. <a href=\"https://doi.org/10.57262/die/1487386822\">https://doi.org/10.57262/die/1487386822</a>.","apa":"Killip, R., Murphy, J., Vişan, M., &#38; Zheng, J. (2017). The focusing cubic NLS with inverse-square potential in three space dimensions. <i>Differential and Integral Equations</i>. Khayyam Publishing. <a href=\"https://doi.org/10.57262/die/1487386822\">https://doi.org/10.57262/die/1487386822</a>","short":"R. Killip, J. Murphy, M. Vişan, J. Zheng, Differential and Integral Equations 30 (2017) 161–206.","mla":"Killip, Rowan, et al. “The Focusing Cubic NLS with Inverse-Square Potential in Three Space Dimensions.” <i>Differential and Integral Equations</i>, vol. 30, no. 3/4, Khayyam Publishing, 2017, pp. 161–206, doi:<a href=\"https://doi.org/10.57262/die/1487386822\">10.57262/die/1487386822</a>.","ama":"Killip R, Murphy J, Vişan M, Zheng J. The focusing cubic NLS with inverse-square potential in three space dimensions. <i>Differential and Integral Equations</i>. 2017;30(3/4):161-206. doi:<a href=\"https://doi.org/10.57262/die/1487386822\">10.57262/die/1487386822</a>"},"extern":"1","article_processing_charge":"No","publisher":"Khayyam Publishing","date_published":"2017-03-01T00:00:00Z","oa":1,"author":[{"full_name":"Killip, Rowan","first_name":"Rowan","last_name":"Killip"},{"last_name":"Murphy","first_name":"Jason","full_name":"Murphy, Jason"},{"id":"056daca0-b8d1-11f0-964f-f91054abf8ca","last_name":"Visan","first_name":"Monica","full_name":"Visan, Monica"},{"full_name":"Zheng, Jiqiang","first_name":"Jiqiang","last_name":"Zheng"}],"arxiv":1,"abstract":[{"lang":"eng","text":"We consider the focusing cubic nonlinear Schrödinger equation with inverse-square potential in three space dimensions. We identify a sharp threshold between scattering and blowup, establishing a result analogous to that of Duyckaerts, Holmer, and Roudenko for the standard focusing cubic NLS. We also prove failure of uniform space-time bounds at the threshold."}],"day":"01","doi":"10.57262/die/1487386822","article_type":"original","issue":"3/4","OA_type":"green","volume":30,"publication_status":"published","month":"03","date_updated":"2026-07-01T12:42:38Z","status":"public","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1603.08912"}],"quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"22088","oa_version":"Preprint","page":"161-206","mathsc":["35Q55"],"language":[{"iso":"eng"}],"publication":"Differential and Integral Equations","scopus_import":"1","type":"journal_article","OA_place":"repository"}]