{"paper":{"title":"Long-time behaviour of two-dimensional Navier-Stokes equations in the presence of Couette flow on the half plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nader Masmoudi, Ning Liu, Weiren Zhao","submitted_at":"2026-05-20T19:15:11Z","abstract_excerpt":"In this paper, we study the long-time behavior of solutions to the two-dimensional Navier-Stokes equations in the presence of Couette flow on the half plane with Navier-slip boundary conditions. We prove that the total vorticity will approach\n  \\begin{align*}\n  -1+\\frac{M_2(\\omega_{0})}{\\nu^{3/2}(1+t)^{5/2}} \\bar{\\Omega}\\left( \\frac{x}{\\sqrt{\\nu(1+t)^3}}, \\frac{y}{\\sqrt{\\nu(1+t)}} \\right),\n  \\end{align*}\n  where $-1$ is the vorticity of the Couette flow and $\\bar{\\Omega}$ is the kernel of a Fokker-Planck type operator $\\mathcal{L}=\\partial_Y^2+\\frac32 X\\partial_X+\\frac12 Y\\partial_Y+\\frac52-Y\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21663","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/2605.21663/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"}