{"paper":{"title":"On the stability of symmetric flows in a two-dimensional channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Bernard Helffer, Yaniv Almog","submitted_at":"2022-12-24T23:05:35Z","abstract_excerpt":"We consider the stability of symmetric flows in a two-dimensional\n  channel (including the Poiseuille flow). In 2015 Grenier, Guo, and\n  Nguyen have established instability of these flows in a particular\n  region of the parameter space, affirming formal asymptotics results\n  from the 1940's. We prove that these flows are stable outside this\n  region in parameter space. More precisely we show that the\n  Orr-Sommerfeld operator\n  $$ {\\mathcal B} =\\Big(-\\frac{d^2}{dx^2}+i\\beta(U+i\\lambda)\\Big)\\Big(\\frac{d^2}{dx^2}-\\alpha^2\\Big) -i\\beta U^{\\prime\\prime}\\,, $$\n  which is defined on $$\n  D({\\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.12827","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/2212.12827/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"}