Asymptotic behavior of solutions of stochastic evolution equations for second grade fluids

Paul André Razafimandimby; Mamadou Sango

doi:10.1016/j.crma.2010.05.001

Partial Differential Equations/Probability Theory

Asymptotic behavior of solutions of stochastic evolution equations for second grade fluids
[Comportement asymptotique des solutions d'équations d'évolution stochastiques des fluides de grade deux]

Présenté par : Pierre-Louis Lions

Paul André Razafimandimby ¹ ; Mamadou Sango ¹

¹ Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa

Comptes Rendus. Mathématique, Volume 348 (2010) no. 13-14, pp. 787-790.

Résumé
Abstract

Dans cette Note nous montrons que, sous des hypothèses appropriées sur les données, on peut construire une suite de solutions fortes des équations stochastiques pour les fluides de grade deux qui convergent vers les solutions fortes probabilistes des équations stochastiques de Navier–Stokes quand le module de contrainte α tend vers zéro.

In this Note we show that under suitable conditions on the data we can construct a sequence of solutions of the stochastic second grade fluid that converges to the probabilistic strong solution of the stochastic Navier–Stokes equations when the stress modulus α tends to zero.

Reçu le : 2010-01-10
Accepté le : 2010-04-27
Publié le : 2010-06-17

DOI : 10.1016/j.crma.2010.05.001

Affiliations des auteurs :

Paul André Razafimandimby ¹ ; Mamadou Sango ¹

¹ Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa

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     title = {Asymptotic behavior of solutions of stochastic evolution equations for second grade fluids},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {787--790},
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     year = {2010},
     doi = {10.1016/j.crma.2010.05.001},
     language = {en},
}

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Paul André Razafimandimby; Mamadou Sango. Asymptotic behavior of solutions of stochastic evolution equations for second grade fluids. Comptes Rendus. Mathématique, Volume 348 (2010) no. 13-14, pp. 787-790. doi : 10.1016/j.crma.2010.05.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.05.001/

Bibliographie
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[11] P.A. Razafimandimby, M. Sango, Weak solutions of a stochastic model for two-dimensional second grade fluids, Boundary Value Problems, vol. 2010, Article ID 636140, p. 47

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