{"paper":{"title":"Decay estimates for the two-dimensional Beam equation with potentials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Han Cheng, Shuangshuang Chen, Xiaohua Yao, Zijun Wan","submitted_at":"2026-06-15T14:36:47Z","abstract_excerpt":"This paper establishes time decay estimates for the following two-dimensional beam (plate) equation with a decaying real-valued potential $V$: \\begin{equation*} \\partial_t^2 u + (\\Delta^2 + V) u = 0, \\qquad u(0,x)=f(x),\\quad \\partial_t u(0,x)=g(x). \\end{equation*} When zero is a regular point or a first-kind resonance of $H=\\Delta^2+V$, we first prove sharp $L^1\\to L^\\infty$ estimates for the solution operators: \\begin{align*} \\left\\|\\cos(t\\sqrt{H})P_{\\mathrm{ac}}(H)\\right\\|_{L^1\\to L^\\infty} + \\left\\|\\frac{\\sin(t\\sqrt{H})}{t\\sqrt{H}}P_{\\mathrm{ac}}(H)\\right\\|_{L^1\\to L^\\infty} \\lesssim \\frac{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.16793","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.16793/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}