Convergence of a sequence of solutions of the stochastic two-dimensional equations of second grade fluids

Article type: Research Article

Authors: Razafimandimby, Paul André^; | Sango, Mamadou^;

Affiliations: Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa. E-mails: prazafim@ictp.it, paul.razafim@gmail.com, sango1767@gmail.com

Note: [] Current address: Mathematics Section, The Abdus Salam International Center for Theoretical Physics, Strada Costiera, 11, I-34151 Trieste, Italy.

Note: [] Corresponding author. E-mail: sango1767@gmail.com

Abstract: We study the limit of the stochastic model for two dimensional second grade fluids subjected to the periodic boundary conditions as the stress modulus tends to zero. We show that under suitable conditions on the data the whole sequence of strong probabilistic solutions (uα) of the stochastic second grade fluid converges to the unique strong probabilistic solution of the stochastic Navier–Stokes equations.

Keywords: stochastic second-grade fluids, tightness, strong and weak probabilistic solutions, asymptotic behavior

DOI: 10.3233/ASY-2012-1095

Journal: Asymptotic Analysis, vol. 79, no. 3-4, pp. 251-272, 2012