{"paper":{"title":"Critical scattering for the nonlinear Schr\\\"odinger equation on waveguide manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Yongming Luo","submitted_at":"2025-05-31T07:49:29Z","abstract_excerpt":"We study the small data scattering problem in critical spaces for the nonlinear Schr\\\"odinger equation (NLS) on waveguide manifolds. Our work is primarily inspired by the recent paper of Kwak and Kwon \\cite{KwakKwon} that established the local well-posedness of the periodic NLS with possibly non-algebraic nonlinearity. While we adopt a framework similar to \\cite{KwakKwon} for our problem, two main obstacles prevent its direct adaptation to the waveguide setting. First, the classical Strichartz estimates for NLS in critical product spaces, introduced by Hani and Pausader, possess limited endpoi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00442","kind":"arxiv","version":2},"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/2506.00442/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"}