{"paper":{"title":"Global Regularity of Axisymmetric Navier-Stokes Equations with NHL Boundary Conditions under a Critical Smallness Condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tsz-Lik Chan","submitted_at":"2026-05-18T08:05:41Z","abstract_excerpt":"We investigate the global regularity problem for the three-dimensional incompressible Navier-Stokes equations restricted to axisymmetric flows in a finite cylinder $D = \\{(r,\\theta,x_3): 0 \\le r \\le 1, 0 \\le \\theta < 2\\pi, 0 \\le x_3 \\le 1\\}$, subject to the Navier-Hodge-Lions (NHL) boundary condition. While global existence of smooth solutions is known in the swirl-free case, the presence of swirl ($v_\\theta \\neq 0$) introduces vortex stretching that may potentially lead to finite-time singularity formation. In this work, we prove that if the initial data satisfy a scaling-invariant smallness "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18011","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.18011/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T23:33:35.529990Z","status":"skipped","version":"1.0.0","findings_count":0}],"snapshot_sha256":"4d6f99380c0f0d568aad29ebeb8a9a0b488aee962b35c4d1506bcf06d04ec847"},"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"}