{"paper":{"title":"A Centre-Stable Manifold for the Energy-Critical Wave Equation in R^3 in the Symmetric Setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Marius Beceanu","submitted_at":"2012-12-11T03:06:38Z","abstract_excerpt":"Consider the focusing semilinear wave equation in R^3 with energy-critical nonlinearity\n  \\partial_t^2 \\psi - \\Delta \\psi - \\psi^5 = 0, \\psi(0) = \\psi_0, \\partial_t \\psi(0) = \\psi_1.\n  This equation admits stationary solutions of the form \\phi(x, a) := (3a)^{1/4} (1+a|x|^2)^{-1/2}, called solitons, which solve the elliptic equation -\\Delta \\phi - \\phi^5 = 0.\n  Restricting ourselves to the space of symmetric solutions \\psi for which \\psi(x) = \\psi(-x), we find a local centre-stable manifold, in a neighborhood of \\phi(x, 1), for this wave equation in the weighted Sobolev space <x>^{-1} \\dot H^1 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2285","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"}