Self-improving bounds for the Navier-Stokes equations

Jean-Yves Chemin (1) , Fabrice Planchon (2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 LJAD - Laboratoire Jean Alexandre Dieudonné

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.

Domaines: Equations aux dérivées partielles [math.AP]

Jean-Yves Chemin, Fabrice Planchon. Self-improving bounds for the Navier-Stokes equations. Bull. Soc. Math. France, 2013, 140 (4), pp.583-597. ⟨10.24033/bsmf.2638⟩. ⟨hal-00936366⟩