{"paper":{"title":"Stability for two-dimensional plane Couette flow to the incompressible Navier-Stokes equations with Navier boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Shijin Ding, Zhilin Lin","submitted_at":"2017-10-13T09:37:44Z","abstract_excerpt":"This paper concerns with the stability of the plane Couette flow resulted from the motions of boundaries that the top boundary $\\Sigma_1$ and the bottom one $\\Sigma_0$ move with constant velocities $(a,0)$ and $(b,0)$, respectively. If one imposes Dirichlet boundary condition on the top boundary and Navier boundary condition on the bottom boundary with Navier coefficient $\\alpha$, there always exists a plane Couette flow which is exponentially stable for nonnegative $\\alpha$ and any positive viscosity $\\mu$ and any $a, b \\in \\mathbb{R}$, or, for $\\alpha<0$ but viscosity $\\mu$ and the moving ve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.04855","kind":"arxiv","version":3},"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/1710.04855/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"}