  We study a mutually coupled mesoscopic-macroscopic-shell system of equations
modeling a dilute incompressible polymer fluid which is evolving and
interacting with a flexible shell of Koiter type. The polymer constitutes a
solvent-solute mixture where the solvent is modelled on the macroscopic scale
by the incompressible Navier-Stokes equation and the solute is modelled on the
mesoscopic scale by a Fokker-Planck equation (Kolmogorov forward equation) for
the probability density function of the bead-spring polymer chain
configuration. This mixture interacts with a nonlinear elastic shell which
serves as a moving boundary of the physical spatial domain of the polymer
fluid. We use the classical model by Koiter to describe the shell movement
which yields a fully nonlinear fourth order hyperbolic equation. Our main
result is the existence of a weak solution to the underlying system which
exists until the Koiter energy degenerates or the flexible shell approaches a
self-intersection.
