Navier-Stokes limit of Jeffreys type flows

We analyze a Jeffreys type model ruling the motion of a viscoelastic polymeric solution with linear memory in a two-dimensional domain with nonslip boundary conditions. For fixed values of the concentrations, we describe the asymptotic dynamics and we prove that, when the scaling parameter in the memory kernel (physically, the Weissenberg number of the flow) tends to zero, the model converges in an appropriate sense to the Navier-Stokes equations.