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Comptes Rendus Mathématique
Volume 334, n° 4
pages 289-292 (2002)
Doi : S1631-073X(02)02255-0
accepted : 17 December 2001
Non-explosion en temps grand et stabilité de solutions globales des équations de Navier-Stokes
Non-blowup at large times and stability for global solutions to the Navier-Stokes equations
 

Isabelle Gallagher a , Dragoş Iftimie a, b , Fabrice Planchon c
a Centre de mathématiques, UMR 7640, École polytechnique, 91128 Palaiseau, France 
b IRMAR, UMR 6625, Université de Rennes 1, campus de Beaulieu, 35042 Rennes, France 
c Laboratoire d'analyse numérique, UMR 7598, boîte 187, Université Paris-VI, 4, place Jussieu, 75252 Paris cedex 05, France 

Note présentée par Jean-Michel Bony

Résumé

Nous nous donnons a priori une solution globale des équations de Navier-Stokes incompressibles dans R3, dans la classe Ct(Ḣ1/2). Nous montrons successivement que la norme Ḣ1/2 tend vers 0 à l'infini, que cette norme contrôle la norme L2t(Ḣ3/2), et qu'une telle solution globale est stable. Pour citer cet article : I. Gallagher et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 289-292.

The full text of this article is available in PDF format.
Abstract

Suppose there exists a global solution u to the incompressible Navier-Stokes equations, such that uCt(Ḣ1/2). We prove that its Ḣ1/2 norm goes to 0 at infinity. We next use this fact to control the L2t(Ḣ3/2) norm of u , and finally we prove that such a solution is stable. To cite this article: I. Gallagher et al., C. R. Acad. Sci. Paris, Ser. I 334 (2002) 289-292.

The full text of this article is available in PDF format.


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