  We prove the existence of weak solutions and a unique strong solution to the
Oldroyd-B dumbbell model describing the evolution of a two-dimensional dilute
polymer fluid interacting with a one-dimensional viscoelastic shell. The
polymer fluid consists of a mixture of an incompressible viscous solvent and a
solute comprising two massless beads connected with Hookean springs. This
solute-solvent mixture then interacts with a flexible structure that evolves in
time. An arbitrary nondegenerate reference domain for the polymer fluid is
allowed and both solutions exist globally in time provided no self-intersection
of the structure occurs.
