{"paper":{"title":"Divergent solutions to the 5D Hartree Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daomin Cao, Qing Guo","submitted_at":"2011-01-11T06:54:35Z","abstract_excerpt":"We consider the Cauchy problem for the focusing Hartree equation $iu_{t}+\\Delta u+(|\\cdot|^{-3}\\ast|u|^{2})u=0$ in $\\mathbb{R}^{5}$ with the initial data in $H^1$, and study the divergent property of infinite-variance and nonradial solutions. Letting $Q$ be the ground state solution of $-Q+\\Delta Q+(|\\cdot|^{-3}\\ast|Q|^{2})Q=0 $ in $ \\mathbb{R}^{5}$, we prove that if $u_{0}\\in H^{1}$ satisfying $M(u_0) E(u_0)<M(Q) E(Q)$ and\n  $\\|\\nabla u_{0}\\|_{2}\\|u_{0}\\|_{2} >\\|\\nabla Q\\|_{2}\\|Q\\|_{2} ,$ then the corresponding solution $u(t)$ either blows up in finite forward time, or exists globally for pos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2053","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"}