On the global existence for a fluid-structure model with small data

We address the system of partial differential equations modeling motion of an elastic body interacting with an incompressible fluid. The fluid is modeled by the incompressible Navier-Stokes equations while the structure is represented by a damped wave equation with no added stabilization terms. We prove global existence and exponential decay of strong solutions for small initial data in a suitable Sobolev space. The elastic displacement is controlled using a new almost divergence-free corrector in the fluid domain. Our approach allows for any superlinear perturbation of the wave equation.