{"paper":{"title":"Scattering for the focusing $L^{2}$ -supercritical and $\\dot H^2$-subcritical biharmonic NLS Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qing Guo","submitted_at":"2015-04-11T09:24:10Z","abstract_excerpt":"We consider the focusing $\\dot H^{s_c}$-critical biharmonic Schr\\\"odinger equation, and prove a global wellposedness and scattering result for the radial data $u_0\\in H^2(\\mathbb R^N)$ satisfying $ M(u_0)^{\\frac{2-s_c}{s_c}}E(u_0)<M(Q)^{\\frac{2-s_c}{s_c}}E(Q) $ and $ \\|u_{0}\\|^{\\frac{2-s_c}{s_c}}_{2}\\|\\Delta u_{0}\\|_{2}<\\|Q\\|^{\\frac{2-s_c}{s_c}}_{2}\\|\\Delta Q\\|_{2}, $ where $s_c\\in(0,2)$ and $Q$ is the ground state of $\\Delta^2Q+(2-s_c)Q-|Q|^{p-1}Q=0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02853","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"}