{"paper":{"title":"On possible isolated blow-up phenomena of the 3D-Navier-Stokes equation and a regularity criterion in terms of supercritical function space condition and smoothness condition along the streamlines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chi Hin Chan, Tsuyoshi Yoneda","submitted_at":"2010-11-26T19:29:01Z","abstract_excerpt":"The first goal of our paper is to give a new type of regularity criterion for solutions $u$ to Navier-Stokes equation in terms of some supercritical function space condition $u \\in L^{\\infty}(L^{\\alpha ,*})$ (with $\\frac{3}{4}(17^{\\frac{1}{2}} -1)< \\alpha < 3 $) and some exponential control on the growth rate of $\\dv (\\frac{u}{|u|})$ along the streamlines of u. This regularity criterion greatly improves the previous one in \\cite{smoothnesscriteria}. The proof leading to the regularity criterion of our paper basically follows the one in \\cite{smoothnesscriteria}. However, we also point out that"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5863","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"}