  The system under study is a solute-solvent-structure (SSS) interaction
problem for the interaction of a dilute three-dimensional Oldroyd-B polymeric
fluid with a two-dimensional viscoelastic shell. We show that a unique global
strong solution to this system exists under the condition that the classical
Ladyzhenskaya--Prodi--Serrin criterion holds for the velocity field and that
the shell displacement is essentially bounded in time with values in the space
of continuously differentiable functions. No requirement is needed for the
polymer number density and the extra stress tensor for the solute component.
