Existence of a solution to a fluid–multi-layered-structure interaction problem

Abstract

We study a nonlinear, unsteady, moving boundary, fluid–structure interaction (FSI) problem in which the structure is composed of two layers: a thick layer, and a thin layer which serves as a fluid–structure interface with mass. The fluid flow, which is driven by the time-dependent dynamic pressure data, is modeled by the Navier–Stokes equations for an incompressible, viscous fluid, defined on a 2D cylinder. The elastodynamics of the cylinder wall is governed by the 1D linear wave equation modeling the thin structural layer, and by the 2D equations of linear elasticity modeling the thick structural layer. We prove existence of a weak solution to this nonlinear FSI problem as long as the cylinder radius is greater than zero. The spaces of weak solutions presented in this manuscript reveal a striking new feature: the presence of a thin fluid–structure interface with mass regularizes solutions of the coupled problem.