{"paper":{"title":"A sharp lower bound for the lifespan of small solutions to the Schr\\\"odinger equation with a subcritical power nonlinearity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hideaki Sunagawa, Shunsuke Yasuda, Yuji Sagawa","submitted_at":"2017-03-09T04:04:07Z","abstract_excerpt":"Let $T_{\\epsilon}$ be the lifespan for the solution to the Schr\\\"odinger equation on $\\mathbb{R}^d$ with a power nonlinearity $\\lambda |u|^{2\\theta/d}u$ ($\\lambda \\in \\mathbb{C}$, $0<\\theta<1$) and the initial data in the form $\\epsilon \\varphi(x)$. We provide a sharp lower bound estimate for $T_{\\epsilon}$ as $\\epsilon \\to +0$ which can be written explicitly by $\\lambda$, $d$, $\\theta$, $\\varphi$ and $\\epsilon$. This is an improvement of the previous result by H.Sasaki [Adv. Diff. Eq. 14 (2009), 1021--1039]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03125","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"}