Exact controllability of a Faedo-Galerkin scheme for the dynamics of polymer fluids

We describe the dynamics of fluids with scattered polymer chains through a multi-field model accounting for weakly non-local inertia and second-neighborhood interactions due to chain entanglements; viscous effects appear at both macroscopic and polymer representations. We consider a linearized version of the pertinent balance equations. For it we prove exact controllability of the pertinent Faedo-Galerkin scheme on the basis of Hilbert's uniqueness method in combination with an appropriate fixed point argument.