{"paper":{"title":"Asymptotic behavior of 2D incompressible ideal flow around small disks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"C. Lacave, H. J. Nussenzveig Lopes, M. C. Lopes Filho","submitted_at":"2015-10-20T12:32:54Z","abstract_excerpt":"In this article, we study the homogenization limit of a family of solutions to the incompressible 2D Euler equations in the exterior of a family of $n_k$ disjoint disks with centers $\\{z^k_i\\}$ and radii $\\varepsilon_k$. We assume that the initial velocities $u_0^k$ are smooth, divergence-free, tangent to the boundary and that they vanish at infinity. We allow, but we do not require, $n_k \\to \\infty$, and we assume $\\varepsilon_k \\to 0$ as $k\\to \\infty$.\n  Let $\\gamma^k_i$ be the circulation of $u_0^k$ around the circle $\\{|x-z^k_i|=\\varepsilon_k\\}$. We prove that the homogenization limit reta"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05864","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"}