{"paper":{"title":"Blow-up criterion of strong solutions to the Navier-Stokes equations in Besov spaces with negative indices","license":"","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Baoquan Yuan, BoZhang","submitted_at":"2007-03-29T14:27:03Z","abstract_excerpt":"A H\\\"older type inequality in Besov spaces is established and applied to show that every strong solution $u(t,x)$ on (0,T) of the Navier-Stokes equations can be continued beyond $t>T$ provided that the vorticity $\\omega(t,x)\\in L^{\\frac 2{2-\\alpha}}(0,T;\\dot{B}^{-\\alpha}_{\\infty,\\infty}(\\mr^3))\\cap L^{\\frac2{1-\\alpha}}(0,T;\\dot{B}^{-1-\\alpha}_{\\infty,\\infty}(\\mr^3))$ for $0<\\alpha<1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0703883","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"}