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

We generalize a classical result of T. Kato on the existence of global solutions to the Navier-Stokes system in C([0,infinity); L-3(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.