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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2507.19106","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-07-25T09:43:12Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f284b42a434876b1ad0fc050a9ee3820dc469fe3b06767555e19fadfb780044d","abstract_canon_sha256":"a5cc2d3248ffe63c12a885692fe98972e48996df4ec9318b0d7ca1bc4b9906fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:43:19.651982Z","signature_b64":"/644gqxZxX3n7LjSKYG/qbwnX6Rq0BPDzy294nDOWI0wydweDSnN7DqrlQU8nal+Gokk8RPW3drBezjzRyCgDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e3bdae866bd1e9c41f8da4e5c7e56bb948f14984060cc1997096c485bac4707","last_reissued_at":"2026-07-05T11:43:19.651518Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:43:19.651518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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