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

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 (u^α) of the stochastic second grade fluid converges to the unique strong probabilistic solution of the stochastic Navier–Stokes equations.