  We study a nonlinear, unsteady, moving boundary, fluid-structure (FSI)
problem in which the structure is composed of two layers: a thin layer which is
in contact with the fluid, and a thick layer which sits on top of the thin
structural layer. The fluid flow, which is driven by the time-dependent dynamic
pressure data, is governed by the 2D 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. The fluid and the structure, as well as the two
structural layers, are fully coupled via the kinematic and dynamic coupling
conditions describing continuity of velocity and balance of contact forces. The
thin structural layer acts as a fluid-structure interface with mass. The
resulting FSI problem is a nonlinear moving boundary problem of
parabolic-hyperbolic type. This problem is motivated by the flow of blood in
elastic arteries whose walls are composed of several layers, each with
different mechanical characteristics and thickness. We prove existence of a
weak solution to this nonlinear FSI problem as long as the cylinder radius is
greater than zero. The proof is based on a novel semi-discrete, operator
splitting numerical scheme, known as the kinematically coupled scheme. We
effectively prove convergence of that numerical scheme to a solution of the
nonlinear fluid-multi-layered-structure interaction problem. 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.
