{"paper":{"title":"Scattering and blow-up criteria for 3D cubic focusing nonlinear inhomogeneous NLS with a potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hua Wang, Qing Guo, Xiaohua Yao","submitted_at":"2018-01-16T09:16:59Z","abstract_excerpt":"In this paper, we consider the 3d cubic focusing inhomogeneous nonlinear Schr\\\"{o}dinger equation with a potential\n  $$\n  iu_{t}+\\Delta u-Vu+|x|^{-b}|u|^{2}u=0,\\;\\;(t,x) \\in {{\\bf{R}}\\times{\\bf{R}}^{3}},\n  $$\n  where $0<b<1$. We first establish global well-posedness and scattering for the radial initial data $u_{0}$ in $H^{1}({\\bf R}^{3})$ satisfying $M(u_{0})^{1-s_{c}}E(u_{0})^{s_{c}}<\\mathcal{E}$ and $\\|u_{0}\\|_{L^{2}}^{2(1-s_{c})}\\|H^{\\frac{1}{2}}u_{0}\\|_{L^{2}}^{2s_{c}}<\\mathcal{K}$ provided that $V$ is repulsive, where $\\mathcal{E}$ and $\\mathcal{K}$ are the mass-energy and mass-kinetic o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.05165","kind":"arxiv","version":3},"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"}