{"paper":{"title":"Dynamics of quintic nonlinear Schr{\\\"o}dinger equations in $H^{2/5+}(\\mathbb{T})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Beno\\^it Gr\\'ebert (LMJL), CNRS), Joackim Bernier (LMJL, Tristan Robert (IECL)","submitted_at":"2023-05-09T07:55:19Z","abstract_excerpt":"In this paper, we succeed in integrating Strichartz estimates (encoding the dispersive effects of the equations) in Birkhoff normal form techniques. As a consequence, we deduce a result on the long time behavior of quintic NLS solutions on the circle for small but very irregular initial data (in $H^s$ for $s > 2/5$). Note that since $2/5 < 1$, we cannot claim conservation of energy and, more importantly, since $2/5 < 1/2$, we must dispense with the algebra property of $H^s$. This is the first dynamical result where we use the dispersive properties of NLS in a context of Birkhoff normal form."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.05236","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.05236/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}