We address a fluid-structure system which consists of the incompressible Navier-Stokes equations and a damped linear wave equation defined on two dynamic domains. The equations are coupled through transmission boundary conditions and additional boundary stabilization effects imposed on the free moving interface separating the two domains. We will discuss local existence and uniqueness of solutions and establish global existence for small initial data. This is a joint work with M. Ignatova, I. Lasiecka, and A. Tuffaha.