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On Stochastic Models Describing the Motions of Randomly Forced Linear Viscoelastic Fluids

This paper is devoted to the analysis of stochastic equations 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 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 fluids that are of great importance in the investigation towards the understanding of the elastic turbulence.