[{"date_created":"2026-06-19T08:47:48Z","scopus_import":"1","quality_controlled":"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.","short":"R. Killip, J. Murphy, M. Vişan, J. Zheng, Differential and Integral Equations 30 (2017) 161–206.","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>","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>.","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.","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>","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>."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","volume":30,"type":"journal_article","year":"2017","issue":"3/4","language":[{"iso":"eng"}],"publication":"Differential and Integral Equations","title":"The focusing cubic NLS with inverse-square potential in three space dimensions","intvolume":"        30","arxiv":1,"page":"161-206","date_published":"2017-03-01T00:00:00Z","mathsc":["35Q55"],"publication_identifier":{"issn":["0893-4983"]},"OA_place":"repository","_id":"22088","publisher":"Khayyam Publishing","publication_status":"published","external_id":{"arxiv":["1603.08912"]},"author":[{"full_name":"Killip, Rowan","first_name":"Rowan","last_name":"Killip"},{"full_name":"Murphy, Jason","first_name":"Jason","last_name":"Murphy"},{"first_name":"Monica","full_name":"Visan, Monica","last_name":"Visan","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"},{"last_name":"Zheng","full_name":"Zheng, Jiqiang","first_name":"Jiqiang"}],"extern":"1","day":"01","doi":"10.57262/die/1487386822","article_processing_charge":"No","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."}],"date_updated":"2026-07-01T12:42:38Z","month":"03","OA_type":"green","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1603.08912"}],"oa":1,"article_type":"original","oa_version":"Preprint","das_tickbox":"1"},{"status":"public","volume":22,"citation":{"short":"M. Vişan, X. Zhang, Differential and Integral Equations 22 (2009) 99–124.","ista":"Vişan M, Zhang X. 2009. Global well-posedness and scattering for a class of nonlinear Schröodinger equations below the energy space. Differential and Integral Equations. 22(1/2), 99–124.","mla":"Vişan, Monica, and Xiaoyi Zhang. “Global Well-Posedness and Scattering for a Class of Nonlinear Schröodinger Equations below the Energy Space.” <i>Differential and Integral Equations</i>, vol. 22, no. 1/2, Khayyam Publishing, 2009, pp. 99–124, doi:<a href=\"https://doi.org/10.57262/die/1356038556\">10.57262/die/1356038556</a>.","ama":"Vişan M, Zhang X. Global well-posedness and scattering for a class of nonlinear Schröodinger equations below the energy space. <i>Differential and Integral Equations</i>. 2009;22(1/2):99-124. doi:<a href=\"https://doi.org/10.57262/die/1356038556\">10.57262/die/1356038556</a>","apa":"Vişan, M., &#38; Zhang, X. (2009). Global well-posedness and scattering for a class of nonlinear Schröodinger equations below the energy space. <i>Differential and Integral Equations</i>. Khayyam Publishing. <a href=\"https://doi.org/10.57262/die/1356038556\">https://doi.org/10.57262/die/1356038556</a>","ieee":"M. Vişan and X. Zhang, “Global well-posedness and scattering for a class of nonlinear Schröodinger equations below the energy space,” <i>Differential and Integral Equations</i>, vol. 22, no. 1/2. Khayyam Publishing, pp. 99–124, 2009.","chicago":"Vişan, Monica, and Xiaoyi Zhang. “Global Well-Posedness and Scattering for a Class of Nonlinear Schröodinger Equations below the Energy Space.” <i>Differential and Integral Equations</i>. Khayyam Publishing, 2009. <a href=\"https://doi.org/10.57262/die/1356038556\">https://doi.org/10.57262/die/1356038556</a>."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","scopus_import":"1","quality_controlled":"1","date_created":"2026-06-19T08:34:09Z","publication":"Differential and Integral Equations","title":"Global well-posedness and scattering for a class of nonlinear Schröodinger equations below the energy space","language":[{"iso":"eng"}],"issue":"1/2","year":"2009","type":"journal_article","date_published":"2009-01-01T00:00:00Z","arxiv":1,"page":"99-124","intvolume":"        22","OA_place":"repository","publication_identifier":{"issn":["0893-4983"]},"mathsc":["35Q55"],"doi":"10.57262/die/1356038556","abstract":[{"text":"We prove global well posedness and scattering for the nonlinear Schröodinger equation with power-type nonlinearity (mathematical formular) below the energy space, i.e., for s<1. In [15], J. Colliander, M. Keel, G. Staffilani, H. Takaoka, and T. Tao established polynomial growth of the \r\nHs/x-norm of the solution, and hence global well posedness for initial data in Hs/x, provided \r\ns is sufficiently close to 1. However, their bounds are insufficient to yield scattering. In this paper, we use the a priori interaction Morawetz inequality to show that scattering holds in H^s(R^n)\r\n whenever s is larger than some value 0<s0(n,p)<1.","lang":"eng"}],"article_processing_charge":"No","day":"01","_id":"22085","publication_status":"published","publisher":"Khayyam Publishing","author":[{"first_name":"Monica","full_name":"Visan, Monica","last_name":"Visan","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"},{"last_name":"Zhang","full_name":"Zhang, Xiaoyi","first_name":"Xiaoyi"}],"external_id":{"arxiv":["math/0606611"]},"extern":"1","OA_type":"green","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.math/0606611"}],"month":"01","date_updated":"2026-07-01T08:33:52Z","oa_version":"Preprint","das_tickbox":"1","oa":1,"article_type":"original"}]