{"paper":{"title":"Improved global well-posedness for the cubic NLS on two-dimensional waveguide $\\R\\times\\T$","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jiqiang Zheng, Kailong Yang, Qionglei Chen, Ruixiao Zhang, Yilin Song","submitted_at":"2024-11-15T07:43:43Z","abstract_excerpt":"In this article, we show that the solution to defocusing cubic nonlinear Schr\\\"odinger equation (NLS) posed on the two-dimensional waveguide \\begin{align*} i\\partial_tu+\\Delta_{\\R\\times\\T}u=|u|^2u \\end{align*} is globally well-posed in $H^s(\\R\\times\\T)$ with $s>\\frac{1}{2}$. The proof is based on the $I$-method. Inspired by Colliander-Keel-Staffilani-Takaoka-Tao [Discrete Contin. Dyn. Syst. 21 (2008), 665-686], we construct the modified energy to improve the energy increment. The main difficulty lies in controlling the resonant interactions caused by the modified energy. To this end, we establ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.10012","kind":"arxiv","version":5},"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/2411.10012/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"}