{"paper":{"title":"The uniform time of existence of the smooth solution for 3D Euler-$\\alpha$ equations with Dirichlet boundary conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Aibin Zang","submitted_at":"2016-04-14T09:11:38Z","abstract_excerpt":"After reformulate the incompressible Euler-$\\alpha$ equations in 3D smooth domain with Drichlet data, we obtain the unique classical solutions to Euler-$\\alpha$ equations exist in uniform time interval independent of $\\alpha$. We also show the solution of the Euler-$\\alpha$ converge to the corresponding solution of Euler equation in $L^2$ in space, uniformly in time. In the sequel, it follows that the $H^s$ $(s>\\frac{n}{2}+1)$ solutions of Euler-$\\alpha$ equations exist in any fixed sub-interval of the maximum existent interval for the Euler equations provided that initial is regular enough an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04083","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"}