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Comptes Rendus Mathématique
Volume 357, n° 2
pages 175-179 (février 2019)
Doi : 10.1016/j.crma.2018.12.007
Received : 10 May 2017 ;  accepted : 1 December 2018
Frequency decay for Navier–Stokes stationary solutions
Décroissance fréquentielle pour les équations de Navier–Stokes stationnaires
 

Diego Chamorro , Oscar Jarrín , Pierre-Gilles Lemarié-Rieusset
 Laboratoire de mathématiques et modélisation d'Évry (LaMME), Université d'Évry-Val-d'Essonne, UMR CNRS 8071, 23, boulevard de France, 91037 Évry cedex, France 

Abstract

We consider stationary Navier–Stokes equations in   with a regular external force and we prove the exponential frequency decay of the solutions. Moreover, if the external force is small enough, we give a pointwise exponential frequency decay for such solutions. If a damping term is added to the equation, a pointwise decay is obtained without the smallness condition over the force.

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

Pour une force extérieure quelconque, mais suffisamment régulière, on démontre la décroissance fréquentielle des solutions de ces équations. Si, de plus, la force est petite, on peut décrire ponctuellement cette décroissance. La condition de petitesse de la force peut être supprimée si l'on rajoute un terme d'amortissement.

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


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