  We analyze a linear 3D/3D fluid-structure interaction problem between a thin
layer of a viscous fluid and a thin elastic plate-like structure with the aim
of deriving a simplified reduced model. Based on suitable energy dissipation
inequalities quantified in terms of two small parameters, thickness of the
fluid layer and thickness of the elastic structure, we identify the right
relation between the system coefficients and small parameters which eventually
provide a reduced model on the vanishing limit. The reduced model is a linear
sixth-order thin-film equation describing the out-of-plane displacement of the
structure, which is justified in terms of weak convergence results relating its
solution to the solutions of the original fluid-structure interaction problem.
Furthermore, approximate solutions to the fluid-structure interaction problem
are reconstructed from the reduced model and quantitative error estimates are
obtained, which provide even strong convergence results.
