[{"oa":1,"article_processing_charge":"No","mathsc":["35Q55"],"month":"02","article_type":"original","date_published":"2019-02-15T00:00:00Z","date_updated":"2026-06-30T07:16:06Z","publication_status":"published","publisher":"Informa UK Limited","das_tickbox":"1","issue":"1","status":"public","year":"2019","OA_place":"repository","publication_identifier":{"issn":["0360-5302"],"eissn":["1532-4133"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","OA_type":"green","title":"Almost sure scattering for the energy-critical NLS with radial data below H1(R4)","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1707.09051","open_access":"1"}],"language":[{"iso":"eng"}],"volume":44,"abstract":[{"text":"We prove almost sure global existence and scattering for the energy-critical nonlinear Schrödinger equation with randomized spherically symmetric initial data in 𝐻𝑠⁡(ℝ4) with \r\n5/6<𝑠<1. We were inspired to consider this problem by the recent work of Dodson–Lührmann–Mendelson, which treated the analogous problem for the energy-critical wave equation.","lang":"eng"}],"day":"15","date_created":"2026-06-19T08:13:26Z","scopus_import":"1","extern":"1","quality_controlled":"1","author":[{"last_name":"Killip","full_name":"Killip, Rowan","first_name":"Rowan"},{"last_name":"Murphy","full_name":"Murphy, Jason","first_name":"Jason"},{"full_name":"Visan, Monica","first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","last_name":"Visan"}],"page":"51-71","doi":"10.1080/03605302.2018.1541904","_id":"22066","type":"journal_article","publication":"Communications in Partial Differential Equations","citation":{"short":"R. Killip, J. Murphy, M. Vişan, Communications in Partial Differential Equations 44 (2019) 51–71.","chicago":"Killip, Rowan, Jason Murphy, and Monica Vişan. “Almost Sure Scattering for the Energy-Critical NLS with Radial Data below H1(R4).” <i>Communications in Partial Differential Equations</i>. Informa UK Limited, 2019. <a href=\"https://doi.org/10.1080/03605302.2018.1541904\">https://doi.org/10.1080/03605302.2018.1541904</a>.","ista":"Killip R, Murphy J, Vişan M. 2019. Almost sure scattering for the energy-critical NLS with radial data below H1(R4). Communications in Partial Differential Equations. 44(1), 51–71.","ama":"Killip R, Murphy J, Vişan M. Almost sure scattering for the energy-critical NLS with radial data below H1(R4). <i>Communications in Partial Differential Equations</i>. 2019;44(1):51-71. doi:<a href=\"https://doi.org/10.1080/03605302.2018.1541904\">10.1080/03605302.2018.1541904</a>","apa":"Killip, R., Murphy, J., &#38; Vişan, M. (2019). Almost sure scattering for the energy-critical NLS with radial data below H1(R4). <i>Communications in Partial Differential Equations</i>. Informa UK Limited. <a href=\"https://doi.org/10.1080/03605302.2018.1541904\">https://doi.org/10.1080/03605302.2018.1541904</a>","mla":"Killip, Rowan, et al. “Almost Sure Scattering for the Energy-Critical NLS with Radial Data below H1(R4).” <i>Communications in Partial Differential Equations</i>, vol. 44, no. 1, Informa UK Limited, 2019, pp. 51–71, doi:<a href=\"https://doi.org/10.1080/03605302.2018.1541904\">10.1080/03605302.2018.1541904</a>.","ieee":"R. Killip, J. Murphy, and M. Vişan, “Almost sure scattering for the energy-critical NLS with radial data below H1(R4),” <i>Communications in Partial Differential Equations</i>, vol. 44, no. 1. Informa UK Limited, pp. 51–71, 2019."},"external_id":{"arxiv":["1707.09051"]},"arxiv":1,"intvolume":"        44"}]