{"article_type":"original","issue":"3","doi":"10.3934/cpaa.2008.7.467","abstract":[{"lang":"eng","text":"We consider the Cauchy problem for a family of semilinear defocusing Schrödinger equations with monomial nonlinearities in one space dimension. We establish global well-posedness and scattering. Our analysis is based on a four-particle interaction Morawetz estimate giving a priori $L_{t,x}^8$ spacetime control on solutions."}],"day":"01","date_published":"2008-03-01T00:00:00Z","author":[{"first_name":"J.","full_name":"Colliander, J.","last_name":"Colliander"},{"last_name":"Holmer","first_name":"Justin","full_name":"Holmer, Justin"},{"first_name":"Monica","full_name":"Visan, Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","last_name":"Visan"},{"full_name":"Zhang, Xiaoyi","first_name":"Xiaoyi","last_name":"Zhang"}],"arxiv":1,"oa":1,"citation":{"short":"J. Colliander, J. Holmer, M. Vişan, X. Zhang, Communications on Pure and Applied Analysis 7 (2008) 467–489.","ama":"Colliander J, Holmer J, Vişan M, Zhang X. Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$. <i>Communications on Pure and Applied Analysis</i>. 2008;7(3):467-489. doi:<a href=\"https://doi.org/10.3934/cpaa.2008.7.467\">10.3934/cpaa.2008.7.467</a>","mla":"Colliander, J., et al. “Global Existence and Scattering for Rough Solutions to Generalized Nonlinear Schrödinger Equations on $R$.” <i>Communications on Pure and Applied Analysis</i>, vol. 7, no. 3, American Institute of Mathematical Sciences, 2008, pp. 467–89, doi:<a href=\"https://doi.org/10.3934/cpaa.2008.7.467\">10.3934/cpaa.2008.7.467</a>.","ieee":"J. Colliander, J. Holmer, M. Vişan, and X. Zhang, “Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$,” <i>Communications on Pure and Applied Analysis</i>, vol. 7, no. 3. American Institute of Mathematical Sciences, pp. 467–489, 2008.","ista":"Colliander J, Holmer J, Vişan M, Zhang X. 2008. Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$. Communications on Pure and Applied Analysis. 7(3), 467–489.","apa":"Colliander, J., Holmer, J., Vişan, M., &#38; Zhang, X. (2008). Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$. <i>Communications on Pure and Applied Analysis</i>. American Institute of Mathematical Sciences. <a href=\"https://doi.org/10.3934/cpaa.2008.7.467\">https://doi.org/10.3934/cpaa.2008.7.467</a>","chicago":"Colliander, J., Justin Holmer, Monica Vişan, and Xiaoyi Zhang. “Global Existence and Scattering for Rough Solutions to Generalized Nonlinear Schrödinger Equations on $R$.” <i>Communications on Pure and Applied Analysis</i>. American Institute of Mathematical Sciences, 2008. <a href=\"https://doi.org/10.3934/cpaa.2008.7.467\">https://doi.org/10.3934/cpaa.2008.7.467</a>."},"extern":"1","article_processing_charge":"No","publisher":"American Institute of Mathematical Sciences","das_tickbox":"1","title":"Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$","year":"2008","date_created":"2026-06-19T08:27:11Z","intvolume":"         7","external_id":{"arxiv":["math/0612452"]},"publication_identifier":{"issn":["1534-0392"],"eissn":["1553-5258"]},"OA_place":"repository","type":"journal_article","scopus_import":"1","publication":"Communications on Pure and Applied Analysis","mathsc":["35Q55"],"language":[{"iso":"eng"}],"_id":"22081","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","page":"467-489","quality_controlled":"1","status":"public","date_updated":"2026-07-01T07:05:55Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.math/0612452"}],"OA_type":"green","volume":7,"publication_status":"published","month":"03"}