In this paper, we consider the interactions between a 2D film of an incompressible viscous fluid deposited on a solid substrate and an elastic 2D structure delimiting the upper boundary of the film. The system is strongly coupled since we assume continuity of velocities and normal stresses at the fluid/structure interface. A general model including a fractional power of the laplacian is chosen to model the structure dynamics. We derive two asymptotic models in the thin film approximation depending on the relative size of the structure mechanical parameters. We then discuss the influence of the power exponent on possible collapse of the film in the various reduced models.

在本文中，我们考虑了沉积在固体基质上的不可压缩粘性流体的2D膜与界定膜的上边界的弹性2D结构之间的相互作用。由于我们假设流体/结构界面处的速度和法向应力具有连续性，因此系统是紧密耦合的。选择包括拉普拉斯分数功率的通用模型来对结构动力学建模。根据结构力学参数的相对大小，我们在薄膜近似中推导了两个渐近模型。然后，我们讨论在各种简化模型中，幂指数对薄膜可能塌陷的影响。