{"paper":{"title":"A sufficient condition for global existence of solutions to a generalized derivative nonlinear Schr\\\"{o}dinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masayuki Hayashi, Noriyoshi Fukaya, Takahisa Inui","submitted_at":"2016-10-02T12:12:25Z","abstract_excerpt":"We give a sufficient condition for global existence of the solutions to a generalized derivative nonlinear Schr\\\"{o}dinger equation (gDNLS) by a variational argument. The variational argument is applicable to a cubic derivative nonlinear Schr\\\"{o}dinger equation (DNLS). For (DNLS), Wu proved that the solution with the initial data $u_0$ is global if $\\left\\Vert u_0 \\right\\Vert_{L^2}^2<4\\pi$ by the sharp Gagliardo--Nirenberg inequality in the paper \"Global well-posedness on the derivative nonlinear Schr\\\"odinger equation\", Analysis & PDE 8 (2015), no. 5, 1101--1112. The variational argument giv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.00267","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":""},"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"}