{"paper":{"title":"Global center stable manifold for the defocusing energy critical wave equation with potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Baoping Liu, Guixiang Xu, Hao Jia, Wilhelm Schlag","submitted_at":"2017-06-27T00:58:58Z","abstract_excerpt":"In this paper we consider the defocusing energy critical wave equation with a trapping potential in dimension $3$. We prove that the set of initial data for which solutions scatter to an unstable excited state $(\\phi, 0)$ forms a finite co-dimensional path connected $C^1$ manifold in the energy space. This manifold is a global and unique center-stable manifold associated with $(\\phi,0)$. It is constructed in a first step locally around any solution scattering to $\\phi$, which might be very far away from $\\phi$ in the $\\dot{H}^1\\times L^2(\\mathbb{R}^3)$ norm. In a second crucial step a no-retur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09284","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"}