{"paper":{"title":"Global existence and scattering for a class of nonlinear fourth-order Schr\\\"odinger equation below the energy space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Van Duong Dinh","submitted_at":"2017-06-21T23:50:31Z","abstract_excerpt":"In this paper, we consider a class of nonlinear fourth-order Schr\\\"odinger equation, namely \\[ \\left\\{ \\begin{array}{rcl} i\\partial_t u +\\Delta^2 u &=&-|u|^{\\nu-1} u, \\quad 1+ \\frac{8}{d}<\\nu <1+\\frac{8}{d-4},\\\\ u(0)&=&u_0 \\in H^\\gamma(\\mathbb{R}^d), \\quad 5 \\leq d \\leq 11. \\end{array} \\right. \\] Using the $I$-method combined with the interaction Morawetz inequality, we establish the global well-posedness and scattering in $H^\\gamma(\\mathbb{R}^d)$ with $\\gamma(d,\\nu)<\\gamma<2$ for some value $\\gamma(d,\\nu)>0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07430","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"}