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Comptes Rendus Mathématique
Volume 352, n° 11
pages 913-915 (novembre 2014)
Doi : 10.1016/j.crma.2014.09.012
Received : 17 August 2014 ;  accepted : 15 September 2014
Some remarks on the paper “On the blow up criterion of 3D Navier–Stokes equations” by J. Benameur
Quelques remarques sur l'article « On the blow up criterion of 3D Navier–Stokes equations » par J. Benameur
 

Pablo Braz e Silva a, Wilberclay G. Melo b, Paulo R. Zingano c
a Departamento de Matemática, Universidade Federal de Pernambuco, Recife, PE 50740, Brazil 
b Departamento de Matemática, Universidade Federal de Sergipe, São Cristóvão, SE 49100, Brazil 
c Departamento de Matemática Pura e Aplicada, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS 91509, Brazil 

Abstract

We indicate some important simplifications and extensions of the analysis recently given by J. Benameur to derive blow-up estimates for strong solutions to 3D incompressible Navier–Stokes equations in homogeneous Sobolev spaces  ,  , in case of finite-time existence.

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Résumé

Nous indiquons quelques simplifications et extensions importantes des résultats obtenus par J. Benameur concernant des estimations inférieures pour l'explosion des solutions fortes des équations de Navier–Stokes incompressibles dans les espaces de Sobolev homogènes  ,  , en cas d'existence non globale.

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