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We analyze a linear 3D/3D fluid-structure interaction problem between a thinlayer of a viscous fluid and a thin elastic plate-like structure with the aimof deriving a simplified reduced model. Based on suitable energy dissipationinequalities quantified in terms of two small parameters, thickness of thefluid layer and thickness of the elastic structure, we identify the rightrelation between the system coefficients and small parameters which eventuallyprovide a reduced model on the vanishing limit. The reduced model is a linearsixth-order thin-film equation describing the out-of-plane displacement of thestructure, which is justified in terms of weak convergence results relating itssolution to the solutions of the original fluid-structure interaction problem.Furthermore, approximate solutions to the fluid-structure interaction problemare reconstructed from the reduced model and quantitative error estimates areobtained, which provide even strong convergence results.

Rigorous derivation of a linear sixth-order thin-film equation as a reduced model for thin fluid -- thin structure interaction problems