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We address the system of partial differential equations modeling motion of anelastic body interacting with an incompressible fluid. The fluid is modeled bythe incompressible Navier-Stokes equations while the structure is representedby a damped wave equation $w_{tt}-\Delta w + \alpha w_t =0$, where $\alpha >0$.We prove the global existence and exponential decay of strong solutions forsmall initial data in a suitable Sobolev space. We show that the elasticvelocity $w_t$ and the acceleration $w_{tt}$ can be controlled by the $H^2$elliptic estimates and by the dissipation of the fluid via the free interface.We also find that, even though the vanishing of the final displacement $w$appears invisible in the energy method, it can be deduced from the preservationof total volume. Our approach allows for any superlinear perturbation of thewave equation.

Global well-posedness and exponential decay for a fluid-structure model with small data