{"paper":{"title":"Enhanced Dissipation and Transition Threshold for the Poiseuille Flow in a Periodic Strip","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Augusto Del Zotto","submitted_at":"2021-08-26T06:52:18Z","abstract_excerpt":"We consider the solution to the 2D Navier-Stokes equations around the Poiseuille flow $(y^2,0)$ on $\\mathbb{T}\\times\\mathbb{R}$ with small viscosity $\\nu>0$. Via a hypocoercivity argument, we prove that the $x-$dependent modes of the solution to the linear problem undergo the enhanced dissipation effect with a rate proportional to $\\nu^{\\frac{1}{2}}$. Moreover, we study the nonlinear enhanced dissipation effect and we establish a transition threshold of $\\nu^{\\frac{2}{3}+}$. Namely, when the perturbation of the Poiseuille flow is size at most $\\nu^{\\frac{2}{3}+}$, its size remains so for all t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.11602","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/2108.11602/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"}