{"paper":{"title":"Global well-posedness and scattering for the energy-critical, defocusing Hartree equation in $\\mathbb{R}^{1+n}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Changxing Miao, Guixiang Xu, Lifeng Zhao","submitted_at":"2007-07-22T11:40:05Z","abstract_excerpt":"Using the same induction on energy argument in both frequency space and spatial space simultaneously as in \\cite{CKSTT07}, \\cite{RyV05} and \\cite{Vi05}, we obtain global well-posedness and scattering of energy solutions of defocusing energy-critical nonlinear Hartree equation in $\\mathbb{R}\\times \\mathbb{R}^n$($n\\geq 5$), which removes the radial assumption on the data in \\cite{MiXZ07a}. The new ingredients are that we use a modified long time perturbation theory to obtain the frequency localization (Proposition \\ref{freqdelocaimplystbound} and Corollary \\ref{frequencylocalization}) of the min"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.3254","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"}