# zbMATH — the first resource for mathematics

Self-improving bounds for the Navier-Stokes equations. (Estimations de bootstrap a priori pour Navier-Stokes.) (English. French summary) Zbl 1260.35105
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.

##### MSC:
 35Q30 Navier-Stokes equations 35B44 Blow-up in context of PDEs
##### Keywords:
Navier-Stokes equations; blow-up criterion; Besov spaces
Full Text: