{"paper":{"title":"Lower bounds on blowing-up solutions of the 3D Navier--Stokes equations in $\\dot H^{3/2}$, $\\dot H^{5/2}$, and $\\dot B^{5/2}_{2,1}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alejandro Vidal-Lopez, David S. McCormick, Eric J. Olson, James C. Robinson, Jose L. Rodrigo, Yi Zhou","submitted_at":"2015-03-14T16:49:28Z","abstract_excerpt":"If $u$ is a smooth solution of the Navier--Stokes equations on ${\\mathbb R}^3$ with first blowup time $T$, we prove lower bounds for $u$ in the Sobolev spaces $\\dot H^{3/2}$, $\\dot H^{5/2}$, and the Besov space $\\dot B^{5/2}_{2,1}$, with optimal rates of blowup: we prove the strong lower bounds $\\|u(t)\\|_{\\dot H^{3/2}}\\ge c(T-t)^{-1/2}$ and $\\|u(t)\\|_{\\dot B^{5/2}_{2,1}}\\ge c(T-t)^{-1}$, but in $\\dot H^{5/2}$ we only obtain the weaker result $\\limsup_{t\\to T^-}(T-t)\\|u(t)\\|_{\\dot H^{5/2}}\\ge c$. The proofs involve new inequalities for the nonlinear term in Sobolev and Besov spaces, both of whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.04323","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"}