{"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 swirl","topic_ref":"56471002f5ad6f04f20e12861588794aa7901ecb598d7f960b48900e00132b59"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"54960aeaedc16638e40aaed7a08c54d12b3bbbeb5b124174117517217805a9bc","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"3919921c9f40651c72d2bd75f8bdee7a77c48d5853243bd96a63ea7f9b577295","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"6_Kx32WOHf5BP1IqSNRLRQu9eWJBFs0_B-V3mY6pKpnhVkEV9Nl6ozo7U-GCsqIR0DCnvlknwpHxynl1h5g5Aw"},"schema":"pubphys.envelope/1"},"record_hash":"54960aeaedc16638e40aaed7a08c54d12b3bbbeb5b124174117517217805a9bc","leaf_index":1620}