Revista Matemática Iberoamericana


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Volume 13, Issue 3, 1997, pp. 515–541
DOI: 10.4171/RMI/229

Published online: 1997-12-31

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

Marco Cannone[1]

(1) Université Paris 7, Paris, France

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.

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Cannone Marco: A generalization of a theorem by Kato on Navier-Stokes equations. Rev. Mat. Iberoam. 13 (1997), 515-541. doi: 10.4171/RMI/229