{"paper":{"title":"On the global well-posedness of the quadratic NLS on $L^2(\\mathbb{R}) + H^1(\\mathbb{T})$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dirk Hundertmark, Leonid Chaichenets, Nikolaos Pattakos, Peer Christian Kunstmann","submitted_at":"2019-04-08T12:56:16Z","abstract_excerpt":"We study the one dimensional nonlinear Schr\\\"odinger equation with power nonlinearity $|u|^{\\alpha - 1} u$ for $\\alpha \\in [1,5]$ and initial data $u_0 \\in L^2(\\mathbb{R}) + H^1(\\mathbb{T})$. We show via Strichartz estimates that the Cauchy problem is locally well-posed. In the case of the quadratic nonlinearity ($\\alpha = 2$) we obtain global well-posedness in the space $C(\\mathbb{R}, L^2(\\mathbb R) + H^1(\\mathbb T))$ via Gronwall's inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04030","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/1904.04030/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"}