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In this work, a result of exponential stability is obtained for solutions ofa compressible flow-structure partial differential equation (PDE) model whichhas recently appeared in the literature. In particular, a compressible flow PDEand its associated state equation for the associated pressure variable, eachevolving within a three dimensional domain $\mathcal{O}$, are coupled to afourth order plate equation which holds on a flat portion $% \Omega $ of theboundary $\partial \mathcal{O}$. Moreover, since this coupled PDE model is theresult of a linearization of the compressible Navier-Stokes equations about anarbitrary state, the flow PDE component contains a generally nonzero ambientflow profile $\mathbf{U}$. By way of obtaining the aforesaid exponentialstability, a \textquotedblleft frequency domain\textquotedblright\ approach isadopted here, an approach which is predicated on obtaining a uniform estimateon the resolvent of the associated flow-structure semigroup generator.

Exponential Stability and Supporting Spectral Analysis of a Linearized Compressible Flow-Structure PDE Model