We generalize a classical result of T. Kato on the existence of global solutions to the Navier-Stokes system in . 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.
Cite this article
Marco Cannone, A generalization of a theorem by Kato on Navier-Stokes equations. Rev. Mat. Iberoam. 13 (1997), no. 3, pp. 515–541DOI 10.4171/RMI/229