Postdoctoral Fellow, Dept of Mathematics, University of Nebraska – Lincoln

**Title: Stability Properties of Nondissipative Compressible Flow-Structure PDE Models**

In this talk, we present recently derived results of uniform stability for a coupled partial differential equation

(PDE) system which models a compressible fluid-structure interaction of current interest within the

mathematical literature. The coupled PDE model under discussion will involve a linearized compressible,

viscous fluid flow evolving within a 3-D cavity, and a linear elastic plate–in the absence of rotational inertia—

which evolves on a portion of the fluid cavity wall. Since the fluid equation component is the result of a careful

linearization of the compressible Navier-Stokes equations about an arbitrary state, this interactive PDE

component will include a nontrivial ambient flow profile, which tends to complicate the analysis. Moreover,

there is an additional coupling PDE which determines the associated pressure variable of the fluid-structure

system. Under a suitable assumption on the ambient vector field, and by obtaining an appropriate estimate for

the associated fluid-structure generator on the imaginary axis, we provide a result of exponential stability for

finite energy solutions of the fluid-structure PDE system.