{"paper":{"title":"Quantitative estimates for uniformly-rotating vortex patches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jaemin Park","submitted_at":"2020-10-14T00:47:21Z","abstract_excerpt":"In this paper, we derive some quantitative estimates for uniformly-rotating vortex patches. We prove that if a non-radial simply-connected patch $D$ is uniformly-rotating with small angular velocity $0 < \\Omega \\ll 1$, then the outmost point of the patch must be far from the center of rotation, with distance at least of order $\\Omega^{-1/2}$. For $m$-fold symmetric simply-connected rotating patches, we show that their angular velocity must be close to $\\frac{1}{2}$ for $m\\gg 1$ with the difference at most $O(1/m)$, and also obtain estimates on $L^{\\infty}$ norm of the polar graph which paramet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.06754","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.06754/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}