{"paper":{"title":"Local energy decay in even dimensions for the wave equation with a time-periodic non-trapping metric and applications to Strichartz estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yavar Kian","submitted_at":"2011-02-21T16:11:39Z","abstract_excerpt":"We obtain local energy decay as well as global Strichartz estimates for the solutions $u$ of the wave equation $\\partial_t^2 u-div_x(a(t,x)\\nabla_xu)=0,\\ t\\in{\\R},\\ x\\in{\\R}^n,$ with time-periodic non-trapping metric $a(t,x)$ equal to $1$ outside a compact set with respect to $x$. We suppose that the cut-off resolvent $R_\\chi(\\theta)=\\chi(\\mathcal U(T, 0)-e^{-i\\theta})^{-1}\\chi$, where $\\mathcal U(T, 0)$ is the monodromy operator and $T$ the period of $a(t,x)$, admits an holomorphic continuation to $\\{\\theta\\in\\mathbb{C}\\ :\\ \\textrm{Im}(\\theta) \\geq 0\\}$, for $n \\geq 3$ , odd, and to $\\{ \\thet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4268","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"}