A linearized viscous, compressible flow-plate interaction with non-dissipative coupling

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 U. In contrast...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2019-09, Vol.477 (1), p.334-356
Main Authors: Avalos, George, Geredeli, Pelin G., Webster, Justin T.
Format: Article
Language:English
Subjects:
Compressible viscous fluid
Fluid-structure interaction
Plate
Semigroup
Well-posedness
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Summary: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 U. In contrast to model in [6], 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 C0-semigroup {eAt}t≥0 on a chosen finite energy space of data. Given this approach, the challenge becomes establishing the maximal dissipativity of an operator A, yielding the flow-structure dynamics.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2019.04.034