Comptes Rendus
no. 6
Partial differential equations
Existence of invariant measures for some damped stochastic dispersive equations
[Existence de mesures invariantes pour des équations dispersives stochastiques]

Présenté par : the Editorial Board

Ibrahim Ekren1 ; Igor Kukavica1 ; Mohammed Ziane2
1 Departement fur Mathematik, ETH Zurich, Ramistrasse 101, CH-8092, Zurich, Switzerland
2 Department of Mathematics, University of Southern California, Los Angeles, CA 90089-2532, USA
Comptes Rendus. Mathématique, Volume 355 (2017) no. 6, pp. 676-679.

On étudie le comportement asymptotique des solutions d'équations dispersives stochastiques amorties, en particulier les équation de KdV et les équations de Schrödinger. Nous montrons que le semi-groupe de transition est Feller et nous établissons l'existence d'une mesure invariante grâce à la propriété de compacité asymptotique du semi-groupe de transition et au critère d'Aldous.

We address the long-time behavior of solutions to damped dispersive stochastic partial differential equations, namely the KdV equation and the nonlinear Schrödinger equation on the whole space. We prove that the transition semigroup is Feller and establish the existence of an invariant measure using the asymptotic compactness property of the transition semigroup and the Aldous criterion.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.04.018
Ibrahim Ekren 1 ; Igor Kukavica 1 ; Mohammed Ziane 2

1 Departement fur Mathematik, ETH Zurich, Ramistrasse 101, CH-8092, Zurich, Switzerland
2 Department of Mathematics, University of Southern California, Los Angeles, CA 90089-2532, USA 
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Ibrahim Ekren; Igor Kukavica; Mohammed Ziane. Existence of invariant measures for some damped stochastic dispersive equations. Comptes Rendus. Mathématique, Volume 355 (2017) no. 6, pp. 676-679. doi : 10.1016/j.crma.2017.04.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.04.018/

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