{"paper":{"title":"Regularization of point vortices for the Euler equation in dimension two","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Daomin Cao, Juncheng Wei, Zhongyuan Liu","submitted_at":"2012-08-15T01:00:54Z","abstract_excerpt":"In this paper, we construct stationary classical solutions of the incompressible Euler equation approximating singular stationary solutions of this equation.\n  This procedure is carried out by constructing solutions to the following elliptic problem [ -\\ep^2 \\Delta u=(u-q-\\frac{\\kappa}{2\\pi}\\ln\\frac{1}{\\ep})_+^p, \\quad & x\\in\\Omega, u=0, \\quad & x\\in\\partial\\Omega, ] where $p>1$, $\\Omega\\subset\\mathbb{R}^2$ is a bounded domain, $q$ is a harmonic function.\n  We showed that if $\\Omega$ is simply-connected smooth domain, then for any given non-degenerate critical point of Kirchhoff-Routh function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3002","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"}