{"paper":{"title":"Energy scattering for a class of the defocusing inhomogeneous nonlinear Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Van Duong Dinh","submitted_at":"2017-10-13T16:49:16Z","abstract_excerpt":"In this paper, we consider a class of the defocusing inhomogeneous nonlinear Schr\\\"odinger equation \\[ i\\partial_t u + \\Delta u - |x|^{-b} |u|^\\alpha u = 0, \\quad u(0)=u_0 \\in H^1, \\] with $b, \\alpha>0$. We firstly study the decaying property of global solutions for the equation when $0<\\alpha<\\alpha^\\star$ where $\\alpha^\\star = \\frac{4-2b}{d-2}$ for $d\\geq 3$. The proof makes use of an argument of Visciglia. We next use this decay to show the energy scattering for the equation in the case $\\alpha_\\star<\\alpha<\\alpha^\\star$, where $\\alpha_\\star = \\frac{4-2b}{d}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05766","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"}