{"paper":{"title":"Regularity Criterion to the axially symmetric Navier-Stokes Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongyi Wei","submitted_at":"2015-08-13T19:38:13Z","abstract_excerpt":"Smooth solutions to the axially symmetric Navier-Stokes equations obey the following maximum principle:$\\|ru_\\theta(r,z,t)\\|_{L^\\infty}\\leq\\|ru_\\theta(r,z,0)\\|_{L^\\infty}.$ We first prove the global regularity of solutions if $\\|ru_\\theta(r,z,0)\\|_{L^\\infty}$ or $ \\|ru_\\theta(r,z,t)\\|_{L^\\infty(r\\leq r_0)}$ is small compared with certain dimensionless quantity of the initial data. This result improves the one in Zhen Lei and Qi S. Zhang \\cite{1}. As a corollary, we also prove the global regularity under the assumption that $|ru_\\theta(r,z,t)|\\leq\\ |\\ln r|^{-3/2},\\ \\ \\forall\\ 0<r\\leq\\delta_0\\in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03318","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"}