{"paper":{"title":"The growth of the vorticity gradient for the two-dimensional Euler flows on domains with corners","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hideyuki Miura, Tsubasa Itoh, Tsuyoshi Yoneda","submitted_at":"2016-02-02T07:48:16Z","abstract_excerpt":"We consider the two-dimensional Euler equations in non-smooth domains with corners. It is shown that if the angle of the corner $\\theta$ is strictly less than $\\pi/2$, the Lipschitz estimate of the vorticity at the corner is at most single exponential growth and the upper bound is sharp. %near the stagnation point. For the corner with the larger angle $\\pi/2 < \\theta <2\\pi$, $\\theta \\neq \\pi$, we construct an example of the vorticity which loses continuity instantaneously. For the case $\\theta \\le \\pi/2$, the vorticity remains continuous inside the domain. We thus identify the threshold of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00815","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"}