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arXiv · 1808.05485

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

George Avalos·Pelin Guven Geredeli·Justin T. Webster
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Abstract

We address semigroup well-posedness for a linear, compressible viscous fluid interacting at its boundary with an elastic plate. We derive the model by linearizing the compressible Navier-Stokes equations about an arbitrary flow state, so the fluid PDE includes an ambient flow profile $\mathbf{U}$. In contrast to model in [Avalos, Geredeli, Webster, 2017], we track the effect of this term at the flow-structure interface, yielding a velocity matching condition involving the material derivative of the structure; this destroys the dissipative nature of the coupling of the dynamics. We adopt here a Lumer-Phillips approach, with a view of associating fluid-structure solutions with a $C_{0}$-semigroup $\left\{e^{\mathcal{A}t}\right\} _{t\geq 0}$ on a chosen finite energy space of data. Given this approach, the challenge becomes establishing the maximal dissipativity of an operator $\mathcal{A}$, yielding the flow-structure dynamics.

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George Avalos, Pelin Guven Geredeli, Justin T. Webster. 2018-08-15. A Linearized Viscous, Compressible Flow-Plate Interaction with Non-dissipative Coupling. https://arxiv.org/abs/1808.05485

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