{"paper":{"title":"Blow-up of critical Besov norms at a potential Navier-Stokes singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fabrice Planchon, Gabriel S. Koch, Isabelle Gallagher","submitted_at":"2014-07-15T21:51:37Z","abstract_excerpt":"We prove that if an initial datum to the incompressible Navier-Stokes equations in any critical Besov space $\\dot B^{-1+\\frac 3p}_{p,q}(\\mathbb{R}^3)$, with $3 <p,q< \\infty$, gives rise to a strong solution with a singularity at a finite time $T>0$, then the norm of the solution in that Besov space becomes unbounded at time $T$. This result, which treats all critical Besov spaces where local existence is known, generalizes the result of Escauriaza, Seregin and Sverak (Uspekhi Mat. Nauk 58(2(350)):3-44, 2003) concerning suitable weak solutions blowing up in $L^3(\\mathbb{R}^3)$. Our proof uses p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4156","kind":"arxiv","version":3},"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"}