On stochastic models describing the motions of randomly forced viscoelastic fluids

Abstract

This paper is devoted to the analysis of a stochastic equation describing the motions of a large class of incompressible linear viscoelastic fluids in two-dimensional subject to periodic boundary condition and driven by random external forces. To do so we distinguish two cases, and for each case a global existence result of probabilistic weak solution for is expounded in this paper. We also prove that under suitable hypotheses on the external random forces the solution turns out to be unique. As concrete examples, we consider the stochastic equations for the Maxwell and Oldroyd uids that are of great importance in the investigation towards the understanding of the elastic turbulence.