{"paper":{"title":"On the convergence rate of the Euler-$\\alpha$, an inviscid second-grade complex fluid, model to the Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Edriss S. Titi, Jasmine S. Linshiz","submitted_at":"2009-11-10T07:36:39Z","abstract_excerpt":"We study the convergence rate of the solutions of the incompressible Euler-$\\alpha$, an inviscid second-grade complex fluid, equations to the corresponding solutions of the Euler equations, as the regularization parameter $\\alpha$ approaches zero. First we show the convergence in $H^{s}$, $s>n/2+1$, in the whole space, and that the smooth Euler-$\\alpha$ solutions exist at least as long as the corresponding solution of the Euler equations. Next we estimate the convergence rate for two-dimensional vortex patch with smooth boundaries."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1846","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"}