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We address semigroup well-posedness for a linear, compressible viscous fluidinteracting at its boundary with an elastic plate. We derive the model bylinearizing the compressible Navier-Stokes equations about an arbitrary flowstate, so the fluid PDE includes an ambient flow profile $\mathbf{U}$. Incontrast to model in [Avalos, Geredeli, Webster, 2017], we track the effect ofthis term at the flow-structure interface, yielding a velocity matchingcondition involving the material derivative of the structure; this destroys thedissipative nature of the coupling of the dynamics. We adopt here aLumer-Phillips approach, with a view of associating fluid-structure solutionswith a $C_{0}$-semigroup $\left\{e^{\mathcal{A}t}\right\} _{t\geq 0}$ on achosen finite energy space of data. Given this approach, the challenge becomesestablishing the maximal dissipativity of an operator $\mathcal{A}$, yieldingthe flow-structure dynamics.

A Linearized Viscous, Compressible Flow-Plate Interaction with Non-dissipative Coupling