{"paper":{"title":"Kolmogorov's Theory of Turbulence and Inviscid Limit of the Navier-Stokes Equations in $\\R^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Gui-Qiang G. Chen, James Glimm","submitted_at":"2010-08-09T17:07:00Z","abstract_excerpt":"We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations in $\\R^3$. We first observe that a pathwise Kolmogorov hypothesis implies the uniform boundedness of the $\\alpha^{th}$-order fractional derivative of the velocity for some $\\alpha>0$ in the space variables in $L^2$, which is independent of the viscosity $\\mu>0$. Then it is shown that this key observation yields the $L^2$-equicontinuity in the time and the uniform bound in $L^q$, for some $q>2$, of the velocity independent of $\\mu>0$. These results lead to the strong convergence of solutions of the Na"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1546","kind":"arxiv","version":2},"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"}