On the stability in weak topology of the set of global solutions to the Navier-Stokes equations - Laboratoire d'Analyse et de Mathématiques Appliquées Accéder directement au contenu
Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2013

On the stability in weak topology of the set of global solutions to the Navier-Stokes equations

Résumé

Let~$X$ be a suitable function space and let~$\cG \subset X$ be the set of divergence free vector fields generating a global, smooth solution to the incompressible, homogeneous three dimensional Navier-Stokes equations. We prove that a sequence of divergence free vector fields converging in the sense of distributions to an element of~$\cG$ belongs to~$\cG$ if~$n$ is large enough, provided the convergence holds ''anisotropically" in frequency space. Typically that excludes self-similar type convergence. Anisotropy appears as an important qualitative feature in the analysis of the Navier-Stokes equations; it is also shown that initial data which does not belong to~$\cG$ (hence which produces a solution blowing up in finite time) cannot have a strong anisotropy in its frequency support.
Fichier principal
Vignette du fichier
bahourigallagher-revised.pdf (474.12 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00624649 , version 1 (19-09-2011)
hal-00624649 , version 2 (22-02-2013)

Identifiants

Citer

Hajer Bahouri, Isabelle Gallagher. On the stability in weak topology of the set of global solutions to the Navier-Stokes equations. Archive for Rational Mechanics and Analysis, 2013. ⟨hal-00624649v2⟩
221 Consultations
254 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More