A generalization of a theorem by Kato on Navier-Stokes equations. (English) Zbl 0897.35061

Cannone, Marco

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)

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