{"paper":{"title":"Vortex Stretching for Axisymmetric Euler Flows Without Swirl: Three-Halves Radial-Moment Growth and Near-Linear Growth of the Vorticity Maximum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daomin Cao, Guolin Qin, Junhong Fan","submitted_at":"2025-11-05T04:39:20Z","abstract_excerpt":"We study long-time vortex stretching for three-dimensional axisymmetric Euler flows without swirl in the head-on collision geometry of anti-parallel vortex rings that motivated Childress's \\(t^{4/3}\\) conjecture [S.~Childress, \\emph{Physica D} \\textbf{237} (2008), 1921--1925] for optimal vorticity growth in the full axisymmetric no-swirl class. For nontrivial compactly supported data that are odd in \\(z\\), nonpositive for \\(z>0\\), and satisfy the hypotheses of the main theorem, we prove \\[\n  \\lim_{t\\to\\infty}\n  \\frac{P(t)[\\log(2+t)]^{5/2}}{(1+t)^{3/2}}=+\\infty,\n  \\qquad\n  P(t):=\\iint_{\\Pi_+}r^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.03171","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2511.03171/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"}