{"paper":{"title":"Exponential growth of the vorticity gradient for the Euler equation on the torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrej Zlatos","submitted_at":"2013-10-23T07:01:07Z","abstract_excerpt":"We prove that there are solutions to the Euler equation on the torus with $C^{1,\\alpha}$ vorticity and smooth except at one point such that the vorticity gradient grows in $L^\\infty$ at least exponentially as $t\\to\\infty$. The same result is shown to hold for the vorticity Hessian and smooth solutions. Our proofs use a version of a recent result by Kiselev and Sverak."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6128","kind":"arxiv","version":2},"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"}