{"paper":{"title":"Capillary gravity water waves linearized at monotone shear flows: eigenvalues and inviscid damping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chongchun Zeng, Xiao Liu","submitted_at":"2021-10-25T02:32:30Z","abstract_excerpt":"This paper is concerned with the eigenvalues and linear inviscid damping of the 2D capillary gravity water waves of finite depth $x_2\\in(-h,0)$ linearized at a monotone shear flow $U(x_2)$. Unlike the linearized Euler equation in a fixed channel where eigenvalues exist only in low horizontal wave number $k$, we first prove the linearized capillary gravity wave has two branches of eigenvalues $-ikc^\\pm(k)$, where the wave speeds $c^\\pm(k)=O(\\sqrt{|k|})$ for $|k|\\gg1$ have the same asymptotics as the those of the linear irrotational capillary gravity waves. Under the additional assumption of $U\""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.12604","kind":"arxiv","version":3},"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/2110.12604/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"}