{"paper":{"title":"Stability of laminar monotone shear flows in a channel for high Reynolds number","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Bernard Helffer, Yaniv Almog","submitted_at":"2025-07-25T09:43:12Z","abstract_excerpt":"We consider the stability of a laminar flow $U\\in C^4([-1,1])$ in the two-dimensional channel $\\mathbb{R} \\times[-1,1]$ in the large Reynolds number limit. Assuming that $U$ is strictly monotone but allowing $U^{\\prime\\prime}$ to vanish, we obtain that if the operator\n  $$\n  {\\mathcal K}_{\\nu}=-\\frac{d^2}{dx^2}+\\frac{U^{\\prime\\prime}}{U-\\nu} \\,, $$ is strictly positive for all $\\nu\\in\\mathbb{R}$ for which $U^{\\prime\\prime}(U^{-1}(\\nu))=0$,then $U$ is stable for sufficiently large Reynolds number. This contribution generalizes previous results mostly by allowing long wave perturbations (but muc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.19106","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.19106/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"}