We generalize a classical result of T. Kato on the existence of global solutions to the Navier-Stokes system in C([0,8);L3(R3)). 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 theory of existence of self-similar solutions for the Navier-Stokes equations.
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