Existence of solution for a micro–macro model of polymeric fluid: the FENE model

We analyse a non-linear micro–macro model of polymeric fluids in the case of a shear flow. More precisely, we consider the FENE dumbbell model, which models polymers by nonlinear springs, accounting for the finite extensibility of the polymer chain. We prove the existence of a unique solution to the stochastic differential equation which rules the evolution of a representative polymer in the flow and next deduce a local-in-time existence and uniqueness result on the system coupling the stochastic differential equation and the momentum equation on the fluid.