{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"94eb221a5fe32a746e8c8dbadfec5d359245608fc07384f381a23c0014e84d69","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011","92cecb10c8fcf9101f272a0e8d91b06b5774bf56da122cb08a4cfaf0c58eb8ec"],"salt":"b54d77111dfba4035090a543c4965ac882d513fa6ddb32ea5c9c39e7bc58f18e","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"mathph.fluid-singularities.axisymmetric-swirl-ns","kind":"well-posed","literature_status":"open","n":"1","parents":[{"note":"","parent_revision":"92cecb10c8fcf9101f272a0e8d91b06b5774bf56da122cb08a4cfaf0c58eb8ec","relation":"special_case"}],"plain":"Flows that are symmetric around an axis but also spin around it are the leading candidates for viscous blowup. Without spin they are known to stay smooth; with spin the question is open even in this restricted class.","posed_since":"","precise":"3D Navier-Stokes on $R^{3}$ with $f = 0$ and smooth, finite-energy, axisymmetric initial data with nonzero swirl $u_{\\theta}$. Prove global regularity, or give smooth axisymmetric data whose solution has limsup_{t -> T} ||u(t)||_inf = infinity. Answer: yes or no with proof; this is a special case of mathph.fluid-singularities.ns-unforced.","problem_ref":null,"references":"","settled_by":"A global regularity proof for all smooth axisymmetric data, or a verified (e.g. computer-assisted) blowup construction in this class without forcing.","status_note":"Hou (arXiv 2107.06509, Foundations of Computational Mathematics) reported numerical evidence of potentially singular axisymmetric flow with maximum vorticity growing by a factor of about $10^{7}$; regularity is proven for zero swirl (Ukhovskii and Yudovich; Ladyzhenskaya, 1968).","title":"Regularity or blowup of axisymmetric Navier-Stokes flows with 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