On the control of viscoelastic Jeffreys fluids

This paper is devoted to analyzing the control of vicoelastic fluids of the Jeffreys kind, also known as Oldroyd models. We will present the interesting problems, with special emphasis in the difficulties that they involve. Then, we will consider appropriate linear approximations and we will establish some partial approximate-finite dimensional controllability results in an arbitrarily small time, with distributed or boundary controls supported by arbitrarily small sets. The proofs rely on some specific unique continuation properties which are implied by the structure of the solutions.