Self-improving bounds for the Navier-Stokes equations
Jean-Yves Chemin, Fabrice Planchon (2012)
Bulletin de la Société Mathématique de France
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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 . Our results rely on turning a priori bounds for the solution in negative Besov spaces into bounds in the positive regularity scale.