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