  We consider a nonlinear, free boundary fluid-structure interaction model in a
bounded domain. The viscous incompressible fluid interacts with a nonlinear
elastic body on the common boundary via the velocity and stress matching
conditions. The motion of the fluid is governed by incompressible Navier-Stokes
equations while the displacement of elastic structure is determined by a
nonlinear elastodynamic system with boundary dissipation. The boundary
dissipation is inserted in the velocity matching condition. We prove the global
existence of the smooth solutions for small initial data and obtain the
exponential decay of the energy of this system as well.
