{"paper":{"title":"Dynamics of scaled norms of vorticity for the three-dimensional Navier-Stokes and Euler equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.CD","authors_text":"J. D. Gibbon","submitted_at":"2012-12-04T11:34:05Z","abstract_excerpt":"A series of numerical experiments is suggested for the three-dimensional Navier-Stokes and Euler equations on a periodic domain based on a set of $L^{2m}$-norms of vorticity $\\Omega_{m}$ for $m\\geq 1$. These are scaled to form the dimensionless sequence $D_{m}= (\\varpi_{0}^{-1}\\Omega_{m})^{\\alpha_{m}}$ where $\\varpi_{0}$ is a constant frequency and $\\alpha_{m} = 2m/(4m-3)$. A numerically testable Navier-Stokes regularity criterion comes from comparing the relative magnitudes of $D_{m}$ and $D_{m+1}$ while another is furnished by imposing a critical lower bound on $\\int_{0}^{t}D_{m}\\,d\\tau$. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.0684","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"}