{"paper":{"title":"Towards a finite-time singularity of the Navier-Stokes equations. Part 2. Vortex reconnection and singularity evasion","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.flu-dyn","authors_text":"H.K.Moffatt, Yoshifumi Kimura","submitted_at":"2019-03-29T07:54:05Z","abstract_excerpt":"In Part 1 of this work, we have derived a dynamical system describing the approach to a finite-time singularity of the Navier-Stokes equations. We now supplement this system with an equation describing the process of vortex reconnection at the apex of a pyramid, neglecting core deformation during the reconnection process. On this basis, we compute the maximum vorticity $\\omega_{max}$ as a function of vortex Reynolds number $R_\\Gamma$ in the range $2000\\le R_\\Gamma \\le 3400$, and deduce a compatible behaviour\n  $\\omega_{max}\\sim \\omega_{0}\\exp{\\left[1 + 220 \\left(\\log\\left[R_{\\Gamma}/2000\\right"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12382","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"}