{"paper":{"title":"On a class of solutions to the generalized derivative Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Felipe Linares, Gleison N. Santos, Gustavo Ponce","submitted_at":"2017-12-02T20:38:01Z","abstract_excerpt":"In this work we shall consider the initial value problem associated to the generalized derivative Schr\\\"odinger equations \\begin{equation*} \\p_tu=i\\p_x^2u + \\mu\\,|u|^{\\a}\\p_xu, \\hskip10pt x,t\\in\\R, \\hskip5pt 0<\\a \\le 1\\;\\, {\\rm and}\\;\\, |\\mu|=1, \\end{equation*} and \\begin{equation*} \\p_tu=i\\p_x^2u + \\mu\\,\\p_x\\big(|u|^{\\a}u\\big), \\hskip10pt x,t\\in\\R, \\hskip5pt 0<\\a \\le 1\\;\\, {\\rm and}\\;\\, |\\mu|=1. \\end{equation*} Following the argument introduced by Cazenave and Naumkin \\cite{Cazenave} we shall establish the local well-posedness for a class of small data in an appropriate weighted Sobolev space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00663","kind":"arxiv","version":1},"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"}