{"paper":{"title":"Muliti-scale regularity of axisymmetric Navier-Stokes equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daoyuan Fang, Hui Chen, Ting Zhang","submitted_at":"2018-02-25T05:27:07Z","abstract_excerpt":"By applying the delicate \\textit{a priori} estimates for the equations of $(\\Phi,\\Gamma)$, which is introduced in the previous work, we obtain some multi-scale regularity criteria of the swirl component $u^{\\theta}$ for the 3D axisymmetric Navier-Stokes equations. In particularly, the solution $\\mathbf{u}$ can be continued beyond the time $T$, provided that $u^{\\theta}$ satiesfies $$ u^{\\theta} \\in L^{p}_{T}L^{q_{v}}_{v}L^{q_{h},w}_{h},~~\\frac{2}{p}+\\frac{1}{q_{v}}+\\frac{2}{q_{h}}\\leq 1, ~2<q_{h}\\leq\\infty,~\\frac{1}{q_{v}}+\\frac{2}{q_{h}}<1. $$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.08956","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"}