{"paper":{"title":"On the stability of laminar flows between plates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Bernard Helffer, Yaniv Almog","submitted_at":"2019-08-17T18:27:01Z","abstract_excerpt":"Consider a two-dimensional laminar flow between two plates, so that $(x_1,x_2)\\in {\\mathbb R} \\times[-1,1]$, given by ${\\mathbf v}(x_1,x_2)=(U(x_2),0)$, where\n  $U\\in C^4([-1,1])$ satisfies $U^\\prime\\neq0$ in $[-1,1]$. We prove that the flow is linearly stable in the large Reynolds number limit, in two different cases:\n  $\\bullet$ $\\sup_{x\\in[-1,1]} |U\"(x)| + \\sup_{x\\in[-1,1]} |U\"(x)| \\ll\n  \\min_{x\\in[-1,1]}|U^\\prime(x)|$ (nearly Couette flows),\n  $\\bullet$ $U^{\\prime\\prime}\\neq0$ in $[-1,1]$.\n  We assume either no-slip or fixed traction force conditions on the plates, and an arbitrary large ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06328","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/1908.06328/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"}