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.

我们分析了粘性流体的薄层和薄的弹性板状结构之间的线性3D / 3D流体-结构相互作用问题，目的是得出简化的简化模型。基于以两个小参数（流体层的厚度和弹性结构的厚度）量化的合适的能量耗散不等式，我们确定了系统系数和小参数之间的正确关系，这些关系最终提供了消失极限的简化模型。简化模型是一个线性六阶薄膜方程，描述了结构的平面外位移，这是根据弱收敛结果证明的，该收敛结果将其解与原始流固耦合问题的解联系起来。此外，