{"paper":{"title":"The vanishing viscosity limit for 2D Navier-Stokes in a rough domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Christophe Lacave, David G\\'erard-Varet, Fr\\'ed\\'eric Rousset, Toan T. Nguyen","submitted_at":"2017-01-30T20:12:55Z","abstract_excerpt":"We study the high Reynolds number limit of a viscous fluid in the presence of a rough boundary. We consider the two-dimensional incompressible Navier-Stokes equations with Navier slip boundary condition, in a domain whose boundaries exhibit fast oscillations in the form $x_2 = \\varepsilon^{1+\\alpha} \\eta(x_1/\\varepsilon)$, $\\alpha > 0$. Under suitable conditions on the oscillating parameter $\\varepsilon$ and the viscosity $\\nu$, we show that solutions of the Navier-Stokes system converge to solutions of the Euler system in the vanishing limit of both $\\nu$ and $\\varepsilon$. The main issue is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08808","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"}