A generalization of a theorem by Kato on Navier-Stokes equations

Abstract

We generalize a classical result of T. Kato on the existence of global solutions to the Navier-Stokes system in $C(|0,\infty );L^3({\mathbb{R}}^3)$. More precisely, we show that if the initial data are sufficiently oscillating, in a suitable Besov space, then Kato's solution exists globally. As a corollary to this result, we obtain a theorem on existence of self-similar solutions for the Navier-Stokes equations.