Comptes Rendus
no. 12
Probability Theory/Partial Differential Equations
Ergodic properties of highly degenerate 2D stochastic Navier–Stokes equations
[Propriétés ergodiques des équations de Navier–Stokes 2D stochastiques, hautement dégénérées.]

Présenté par : Paul Malliavin

Martin Hairer1 ; Jonathan C. Mattingly2
1 Math Department, The University of Warwick, Coventry CV4 7AL, UK
2 Math Department, Duke University, Box 90320, Durham, NC 27708, USA
Comptes Rendus. Mathématique, Volume 339 (2004) no. 12, pp. 879-882.

Cette Note présente les résultats de l'article « Ergodicity of the degenerate stochastic 2D Navier–Stokes equation » par M. Hairer et J.C. Mattingly. Nous étudions l'équation de Navier–Stokes sur le tore bidimensionel, excitée par un bruit blanc gaussien de dimension finie. Nous donnons des conditions suffisantes pour que la solution soit ergodique. Nos résultats sont en particulier vrais dans certains cas de bruit blanc gaussien de dimension quatre.

This Note presents the results from “Ergodicity of the degenerate stochastic 2D Navier–Stokes equation” by M. Hairer and J.C. Mattingly. We study the Navier–Stokes equation on the two-dimensional torus when forced by a finite dimensional Gaussian white noise and give conditions under which the system is ergodic. In particular, our results hold for specific choices of four-dimensional Gaussian white noise.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.09.035
Martin Hairer 1 ; Jonathan C. Mattingly 2

1 Math Department, The University of Warwick, Coventry CV4 7AL, UK
2 Math Department, Duke University, Box 90320, Durham, NC 27708, USA 
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Martin Hairer; Jonathan C. Mattingly. Ergodic properties of highly degenerate 2D stochastic Navier–Stokes equations. Comptes Rendus. Mathématique, Volume 339 (2004) no. 12, pp. 879-882. doi : 10.1016/j.crma.2004.09.035. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.035/

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