{"paper":{"title":"Dynamics near the subcritical transition of the 3D Couette flow II: Above threshold case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","physics.flu-dyn"],"primary_cat":"math.AP","authors_text":"Jacob Bedrossian, Nader Masmoudi, Pierre Germain","submitted_at":"2015-06-11T16:01:45Z","abstract_excerpt":"This is the second in a pair of works which study small disturbances to the plane, periodic 3D Couette flow in the incompressible Navier-Stokes equations at high Reynolds number $\\textbf{Re}$. In this work, we show that there is constant $0 < c_0 \\ll 1$, independent of $\\textbf{Re}$, such that sufficiently regular disturbances of size $\\epsilon \\lesssim \\textbf{Re}^{-2/3-\\delta}$ for any $\\delta > 0$ exist at least until $t = c_0\\epsilon^{-1}$ and in general evolve to be $O(c_0)$ due to the lift-up effect. Further, after times $t \\gtrsim \\textbf{Re}^{1/3}$, the streamwise dependence of the sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03721","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":""},"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"}