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The solutions constructed are H\\\"older continuous for spatial variables in $\\overline{\\Pi}$ if in addition that $\\omega^{\\theta}_{0}/r\\in L^{s}$ for $s\\in (3,\\infty)$ and unique if $s=\\infty$. The proof is by a vanishing viscosity method. We show that the Navier-Stokes equations subje"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1806.04811","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-13T01:32:38Z","cross_cats_sorted":[],"title_canon_sha256":"2b6c9202c80564ca50d884b95fe249bfbd9f432cbf70c61b6a340e2c14a8b229","abstract_canon_sha256":"5e094d4bb0c0d44e30145fb76ae05dfe2c5f07402659cc760e135a396c5451eb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:53.277122Z","signature_b64":"DDeNaMlUW+x08+2wrP5kUWVwvWkj2xaJsBpogcIXC70nahOI1ZWQToI85ut47yviIWBSYIIR2/EM/EtsJru6Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7a2fc1a758976d2a4d270133d6433052812a1cc5f31a7d7d034cb43f7302ecc","last_reissued_at":"2026-05-17T23:56:53.276706Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:53.276706Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Vanishing viscosity limits for axisymmetric flows with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ken Abe","submitted_at":"2018-06-13T01:32:38Z","abstract_excerpt":"We construct global weak solutions of the Euler equations in an infinite cylinder $\\Pi=\\{x\\in \\mathbb{R}^{3}\\ |\\ x_h=(x_1,x_2),\\ r=|x_h|<1\\}$ for axisymmetric initial data without swirl when initial vorticity $\\omega_{0}=\\omega^{\\theta}_{0}e_{\\theta}$ satisfies $\\omega^{\\theta}_{0}/r\\in L^{q}$ for $q\\in [3/2,3)$. The solutions constructed are H\\\"older continuous for spatial variables in $\\overline{\\Pi}$ if in addition that $\\omega^{\\theta}_{0}/r\\in L^{s}$ for $s\\in (3,\\infty)$ and unique if $s=\\infty$. The proof is by a vanishing viscosity method. 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