{"paper":{"title":"The interctitical defocusing nonlinear Schr\\\"odinger equations with radial initial data in dimensions four and higher","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changxing Miao, Chuanwei Gao, Jianwei Yang","submitted_at":"2017-07-15T04:22:05Z","abstract_excerpt":"In this paper, we consider the defocusing nonlinear Schr\\\"odinger equation in space dimensions $d\\geq 4$. We prove that if $u$ is a radial solution which is \\emph{priori} bounded in the critical Sobolev space, that is, $u\\in L_t^\\infty \\dot{H}^{s_c}_x$, then $u$ is global and scatters. In practise, we use weighted Strichartz space adapted for our setting which ultimately helps us solve the problems in cases $d\\geq 4$ and $0<s_c<\\f{1}{2}$. The results in this paper extend the work of \\cite[Comm. in PDEs, 40(2015), 265-308]{M3} to higher dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04686","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"}