{"paper":{"title":"Sharp Ill-Posedness of the Euler Equations in Lorentz Spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexey Cheskidov, Jeaheang Bang","submitted_at":"2026-05-15T18:00:43Z","abstract_excerpt":"We study vortex stretching for the three-dimensional axisymmetric Euler equations without swirl in vorticity formulation. Danchin (2007) established global existence and uniqueness for bounded vorticity $\\omega_0$ provided $\\omega_0/r$ lies in the endpoint Lorentz space $L^{3,1}(\\mathbb{R}^3)$ (together with a decay assumption on $\\omega_0$). We prove that this $L^{3,1}$ endpoint is sharp: for every Lorentz exponent $q>1$, we construct multi-ring data $\\omega_0 \\in L^\\infty (\\mathbb{R}^3)$ with $\\omega_0/r\\in L^{3,q}(\\mathbb{R}^3)$ that produce $L^\\infty$-norm inflation of the vorticity; moreo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.16502","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/2605.16502/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T19:33:23.094977Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T19:21:56.979947Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"eb85e39c1fc090af66ad34b941a28dd9b23fdb4cf06c5874561c7bbf8c99d085"},"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"}