Dynamics of a nonlinear elastic plate interacting with a linearized compressible viscous fluid

Abstract

We study well-posedness and long time dynamics of a coupled model consisting of the compressible isothermal linearized Navier–Stokes fluid in some 3D domain and a nonlinear elastic plate placed on a part of the boundary. We first prove the existence and uniqueness of solutions of the corresponding initial–boundary value problem in a finite energy space. Our main result states the existence of a global finite-dimensional attractor even in the absence of a mechanical damping applied to the plate.