Some remarks on the paper “On the blow up criterion of 3D Navier–Stokes equations” by J. Benameur

Braz e Silva, Pablo; Melo, Wilberclay G.; Zingano, Paulo R.

doi:10.1016/j.crma.2014.09.012

Partial differential equations

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]

Présenté par : Philippe G. Ciarlet

Braz e Silva, Pablo ¹ ; Melo, Wilberclay G.² ; Zingano, Paulo R.³

¹ Departamento de Matemática, Universidade Federal de Pernambuco, Recife, PE 50740, Brazil
² Departamento de Matemática, Universidade Federal de Sergipe, São Cristóvão, SE 49100, Brazil
³ Departamento de Matemática Pura e Aplicada, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS 91509, Brazil

Comptes Rendus. Mathématique, Tome 352 (2014) no. 11, pp. 913-915.

Résumé
Abstract

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 ${\dot{H}}^{s} (R^{3})$ , $s > 1 / 2$ , en cas d'existence non globale.

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 ${\dot{H}}^{s} (R^{3})$ , $s > 1 / 2$ , in case of finite-time existence.

Reçu le : 2014-08-17
Accepté le : 2014-09-15
Publié le : 2014-10-03

DOI : 10.1016/j.crma.2014.09.012

Affiliations des auteurs :

Braz e Silva, Pablo ¹ ; Melo, Wilberclay G. ² ; Zingano, Paulo R. ³

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Braz e Silva, Pablo; Melo, Wilberclay G.; Zingano, Paulo R. Some remarks on the paper “On the blow up criterion of 3D Navier–Stokes equations” by J. Benameur. Comptes Rendus. Mathématique, Tome 352 (2014) no. 11, pp. 913-915. doi : 10.1016/j.crma.2014.09.012. http://www.numdam.org/articles/10.1016/j.crma.2014.09.012/

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