Self-improving bounds for the Navier-Stokes equations

2011/11/05 by Jean-Yves Chemin, Chemin, Jean-Yves, Fabrice Planchon +1
Mathematics · #35B44 #35Q30 #76D03 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B44 #msc:35Q30 #msc:76D03

paper · pdf · doi:10.48550/arxiv.1111.1356

11 pages, updated references, to appear in Bull. Soc. Math. France

arxiv created 2013/01/04 · arxiv updated 2013/01/07

Abstract

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.

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