Chemin, Jean-Yves; Planchon, Fabrice Self-improving bounds for the Navier-Stokes equations. (Estimations de bootstrap a priori pour Navier-Stokes.) (English. French summary) Zbl 1260.35105 Bull. Soc. Math. Fr. 140, No. 4, 583-597 (2012). Summary: We consider regular solutions to the Navier-Stokes equation and provide an extension to the Escauriaza-Seregin-Sverak blow-up criterion in the negative regularity Besov scale, with regularity arbitrarly close to \(-1\). Our results rely on turning a priori bounds for the solution in negative Besov spaces into bounds in the positive regularity scale. Cited in 5 Documents MSC: 35Q30 Navier-Stokes equations 35B44 Blow-up in context of PDEs Keywords:Navier-Stokes equations; blow-up criterion; Besov spaces PDF BibTeX XML Cite \textit{J.-Y. Chemin} and \textit{F. Planchon}, Bull. Soc. Math. Fr. 140, No. 4, 583--597 (2012; Zbl 1260.35105) Full Text: DOI Link arXiv