{"paper":{"title":"Blowup for fractional NLS","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Dominik Himmelsbach, Enno Lenzmann, Thomas Boulenger","submitted_at":"2015-09-29T16:53:53Z","abstract_excerpt":"We consider fractional NLS with focusing power-type nonlinearity $$i \\partial_t u = (-\\Delta)^s u - |u|^{2 \\sigma} u, \\quad (t,x) \\in \\mathbb{R} \\times \\mathbb{R}^N,$$ where $1/2< s < 1$ and $0 < \\sigma < \\infty$ for $s \\geq N/2$ and $0 < \\sigma \\leq 2s/(N-2s)$ for $s < N/2$. We prove a general criterion for blowup of radial solutions in $\\mathbb{R}^N$ with $N \\geq 2$ for $L^2$-supercritical and $L^2$-critical powers $\\sigma \\geq 2s/N$. In addition, we study the case of fractional NLS posed on a bounded star-shaped domain $\\Omega \\subset \\mathbb{R}^N$ in any dimension $N \\geq 1$ and subject to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08845","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"}