JournalsrmiVol. 13, No. 3pp. 515–541

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

  • Marco Cannone

    Université Paris 7, Paris, France
A generalization of a theorem by Kato on Navier-Stokes equations cover
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Abstract

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

Cite this article

Marco Cannone, A generalization of a theorem by Kato on Navier-Stokes equations. Rev. Mat. Iberoam. 13 (1997), no. 3, pp. 515–541

DOI 10.4171/RMI/229