[{"title":"Scattering for the cubic-quintic NLS: Crossing the virial threshold","scopus_import":"1","oa":1,"article_processing_charge":"No","year":"2021","_id":"22084","month":"01","status":"public","publication":"SIAM Journal on Mathematical Analysis","day":"01","publication_identifier":{"eissn":["1095-7154"],"issn":["0036-1410"]},"publisher":"Society for Industrial & Applied Mathematics","OA_place":"repository","doi":"10.1137/20m1381824","fulldoi":"https://doi.org/10.1137/20m1381824","author":[{"full_name":"Killip, Rowan","first_name":"Rowan","last_name":"Killip"},{"full_name":"Murphy, Jason","first_name":"Jason","last_name":"Murphy"},{"last_name":"Visan","first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","full_name":"Visan, Monica"}],"abstract":[{"lang":"eng","text":"We consider the nonlinear Schrödinger equation in three space dimensions with combined focusing cubic and defocusing quintic nonlinearity. This problem was considered previously by Killip et al. [Arch. Ration. Mech. Anal., 225 (2017), pp. 469--548], who proved scattering for the whole region of the mass/energy plane where the virial quantity is guaranteed to be positive. In this paper, we prove scattering in a slightly larger region where, in particular, the virial quantity is no longer guaranteed to be sign definite."}],"das_tickbox":"1","keyword":["NLS","scattering","viral"],"OA_type":"green","quality_controlled":"1","intvolume":"        53","arxiv":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2026-06-19T08:28:23Z","oa_version":"Preprint","language":[{"iso":"eng"}],"date_published":"2021-01-01T00:00:00Z","type":"journal_article","extern":"1","publication_status":"published","date_updated":"2026-07-01T07:37:46Z","article_type":"original","mathsc":["35Q55"],"volume":53,"issue":"5","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2007.07406","open_access":"1"}],"external_id":{"arxiv":["2007.07406"]},"page":"5803-5812","citation":{"chicago":"Killip, Rowan, Jason Murphy, and Monica Vişan. “Scattering for the Cubic-Quintic NLS: Crossing the Virial Threshold.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial &#38; Applied Mathematics, 2021. <a href=\"https://doi.org/10.1137/20m1381824\">https://doi.org/10.1137/20m1381824</a>.","apa":"Killip, R., Murphy, J., &#38; Vişan, M. (2021). Scattering for the cubic-quintic NLS: Crossing the virial threshold. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial &#38; Applied Mathematics. <a href=\"https://doi.org/10.1137/20m1381824\">https://doi.org/10.1137/20m1381824</a>","mla":"Killip, Rowan, et al. “Scattering for the Cubic-Quintic NLS: Crossing the Virial Threshold.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 53, no. 5, Society for Industrial &#38; Applied Mathematics, 2021, pp. 5803–12, doi:<a href=\"https://doi.org/10.1137/20m1381824\">10.1137/20m1381824</a>.","ista":"Killip R, Murphy J, Vişan M. 2021. Scattering for the cubic-quintic NLS: Crossing the virial threshold. SIAM Journal on Mathematical Analysis. 53(5), 5803–5812.","ama":"Killip R, Murphy J, Vişan M. Scattering for the cubic-quintic NLS: Crossing the virial threshold. <i>SIAM Journal on Mathematical Analysis</i>. 2021;53(5):5803-5812. doi:<a href=\"https://doi.org/10.1137/20m1381824\">10.1137/20m1381824</a>","short":"R. Killip, J. Murphy, M. Vişan, SIAM Journal on Mathematical Analysis 53 (2021) 5803–5812.","ieee":"R. Killip, J. Murphy, and M. Vişan, “Scattering for the cubic-quintic NLS: Crossing the virial threshold,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 53, no. 5. Society for Industrial &#38; Applied Mathematics, pp. 5803–5812, 2021."}}]