{"paper":{"title":"Concentrated steady vorticities of the Euler equation on 2-d domains and their linear stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chongchun Zeng, Yiming Long, Yuchen Wang","submitted_at":"2018-09-17T20:09:26Z","abstract_excerpt":"We consider concentrated vorticities for the Euler equation on a smooth domain $\\Omega \\subset \\mathbf{R}^2$ in the form of \\[ \\omega = \\sum_{j=1}^N \\omega_j \\chi_{\\Omega_j}, \\quad |\\Omega_j| = \\pi r_j^2, \\quad \\int_{\\Omega_j} \\omega_j d\\mu =\\mu_j \\ne 0, \\] supported on well-separated vortical domains $\\Omega_j$, $j=1, \\ldots, N$, of small diameters $O(r_j)$. A conformal mapping framework is set up to study this free boundary problem with $\\Omega_j$ being part of unknowns. For any given vorticities $\\mu_1, \\ldots, \\mu_N$ and small $r_1, \\ldots, r_N\\in \\mathbf{R}^+$, through a perturbation appr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.06425","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":""},"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"}