{"paper":{"title":"A geometric characterization of steady laminar flow","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Marc Nualart, Theodore D. Drivas","submitted_at":"2024-10-24T17:37:29Z","abstract_excerpt":"We study the steady states of the Euler equations on the periodic channel or annulus. We show that if these flows are laminar (layered by closed non-contractible streamlines which foliate the domain), then they must be either parallel or circular flows. We also show that a large subset of these shear flows are isolated from non-shear stationary states. For Poiseuille flow, $(v(y),0)=(y^2,0)$, our result shows that all stationary solutions in a sufficiently small $C^2$ neighborhood are shear flows. We then show that if $v(y)=y^n$ with $n \\geq 1$, then in any $C^{n-}$ neighborhood, there exist s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.18946","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/2410.18946/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"}