{"paper":{"title":"Conditional regularity of solutions of the three dimensional Navier-Stokes equations and implications for intermittency","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":"2011-08-23T16:35:05Z","abstract_excerpt":"Two unusual time-integral conditional regularity results are presented for the three-dimensional Navier-Stokes equations. The ideas are based on $L^{2m}$-norms of the vorticity, denoted by $\\Omega_{m}(t)$, and particularly on $D_{m} = \\Omega_{m}^{\\alpha_{m}}$, where $\\alpha_{m} = 2m/(4m-3)$ for $m\\geq 1$. The first result, more appropriate for the unforced case, can be stated simply : if there exists an $1\\leq m < \\infty$ for which the integral condition is satisfied ($Z_{m}=D_{m+1}/D_{m}$) $$ \\int_{0}^{t}\\ln (\\frac{1 + Z_{m}}{c_{4,m}}) d\\tau \\geq 0$$ then no singularity can occur on $[0, t]$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.4651","kind":"arxiv","version":4},"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"}