{"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","doi":"10.57262/die/1356038556","day":"01","extern":"1","publisher":"Khayyam Publishing","_id":"22085","publication_status":"published","external_id":{"arxiv":["math/0606611"]},"author":[{"last_name":"Visan","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","full_name":"Visan, Monica","first_name":"Monica"},{"last_name":"Zhang","first_name":"Xiaoyi","full_name":"Zhang, Xiaoyi"}],"das_tickbox":"1","oa_version":"Preprint","article_type":"original","oa":1,"OA_type":"green","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.math/0606611","open_access":"1"}],"month":"01","date_updated":"2026-07-01T08:33:52Z","title":"Global well-posedness and scattering for a class of nonlinear Schröodinger equations below the energy space","publication":"Differential and Integral Equations","language":[{"iso":"eng"}],"year":"2009","type":"journal_article","issue":"1/2","volume":22,"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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>.","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.","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>","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.","short":"M. Vişan, X. Zhang, Differential and Integral Equations 22 (2009) 99–124."},"quality_controlled":"1","scopus_import":"1","date_created":"2026-06-19T08:34:09Z","OA_place":"repository","publication_identifier":{"issn":["0893-4983"]},"mathsc":["35Q55"],"date_published":"2009-01-01T00:00:00Z","arxiv":1,"page":"99-124","intvolume":"        22"}