Revista Matemática Iberoamericana
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Published online: 1997-12-31
A generalization of a theorem by Kato on Navier-Stokes equationsMarco Cannone (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