{"paper":{"title":"Continuous dependence for NLS in fractional order spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daoyuan Fang, Thierry Cazenave, Zheng Han","submitted_at":"2010-06-14T15:46:16Z","abstract_excerpt":"We consider the Cauchy problem for the nonlinear Schr\\\"odinger equation\n  $iu_t+ \\Delta u+ \\lambda |u|^\\alpha u=0$ in $\\R^N $, in the $H^s$-subcritical and critical cases $0<\\alpha \\le 4/(N-2s)$, where $0<s<N/2$. Local existence of solutions in $H^s$ is well known. However, even though the solution is constructed by a fixed-point technique, continuous dependence in $H^s$ does not follow from the contraction mapping argument. In this paper, assuming furthermore $s<1$, we show that the solution depends continuously on the initial value in the sense that the local flow is continuous $H^s \\to H^s$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.2745","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":""},"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"}