{"paper":{"title":"Asymptotic stability in the critical space of 2D monotone shear flow in the viscous fluid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hui Li, Weiren Zhao","submitted_at":"2023-06-06T10:10:21Z","abstract_excerpt":"In this paper, we study the long-time behavior of the solutions to the two-dimensional incompressible free Navier Stokes equation (without forcing) with small viscosity $\\nu$, when the initial data is close to stable monotone shear flows. We prove the asymptotic stability and obtain the sharp stability threshold $\\nu^{\\frac{1}{2}}$ for perturbations in the critical space $H^{log}_xL^2_y$. Specifically, if the initial velocity $V_{in}$ and the corresponding vorticity $W_{in}$ are $\\nu^{\\frac{1}{2}}$-close to the shear flow $(b_{in}(y),0)$ in the critical space, i.e., $\\|V_{in}-(b_{in}(y),0)\\|_{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.03555","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/2306.03555/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"}