{"paper":{"title":"The Sobolev stability threshold for 2D shear flows near Couette","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Fei Wang, Jacob Bedrossian, Vlad Vicol","submitted_at":"2016-04-06T23:32:33Z","abstract_excerpt":"We consider the 2D Navier-Stokes equation on $\\mathbb T \\times \\mathbb R$, with initial datum that is $\\varepsilon$-close in $H^N$ to a shear flow $(U(y),0)$, where $\\| U(y) - y\\|_{H^{N+4}} \\ll 1$ and $N>1$. We prove that if $\\varepsilon \\ll \\nu^{1/2}$, where $\\nu$ denotes the inverse Reynolds number, then the solution of the Navier-Stokes equation remains $\\varepsilon$-close in $H^1$ to $(e^{t \\nu \\partial_{yy}}U(y),0)$ for all $t>0$. Moreover, the solution converges to a decaying shear flow for times $t \\gg \\nu^{-1/3}$ by a mixing-enhanced dissipation effect, and experiences a transient grow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01831","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":""},"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"}