{"paper":{"title":"The dynamics of the NLS with the combined terms in five and higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Changxing Miao, Guixiang Xu, Lifeng Zhao","submitted_at":"2011-12-20T09:31:54Z","abstract_excerpt":"In this paper, we continue the study in \\cite{MiaoWZ:NLS:3d Combined} to show the scattering and blow-up result of the solution for the nonlinear Schr\\\"{o}dinger equation with the energy below the threshold $m$ in the energy space $H^1(\\R^d)$, iu_t + \\Delta u = -|u|^{4/(d-2)}u + |u|^{4/(d-1)}u, \\; d\\geq 5. \\tag{CNLS} The threshold is given by the ground state $W$ for the energy-critical NLS: $iu_t + \\Delta u = -|u|^{4/(d-2)}u$. Compared with the argument in \\cite{MiaoWZ:NLS:3d Combined}, the new ingredient is that we use the double duhamel formula in \\cite{Kiv:Clay Lecture, TaoVZ:NLS:mass comp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4618","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"}