Cannone, Marco A generalization of a theorem by Kato on Navier-Stokes equations. (English) Zbl 0897.35061 Rev. Mat. Iberoam. 13, No. 3, 515-541 (1997). The aim of this paper is to prove that Kato’s result, on existence of global solutions to the Navier-Stokes system in \(C([0,\infty); L^3(\mathbb{R}^3))\), holds true under a much weaker condition on the initial data. Furthermore, using the previous result, the author obtains an existence theorem of self-similar solutions for the Navier-Stokes equations. Reviewer: V.A.Sava (Iaşi) Cited in 1 ReviewCited in 115 Documents MSC: 35Q30 Navier-Stokes equations 76D05 Navier-Stokes equations for incompressible viscous fluids 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:Navier-Stokes equation; self-similar solution PDF BibTeX XML Cite \textit{M. Cannone}, Rev. Mat. Iberoam. 13, No. 3, 515--541 (1997; Zbl 0897.35061) Full Text: DOI EuDML OpenURL