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


Avalos G., Geredeli P. G. , Webster J. T.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.477, no.1, pp.334-356, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 477 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.1016/j.jmaa.2019.04.034
  • Title of Journal : JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Page Numbers: pp.334-356

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 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 C-0-semigroup {e(At)}(t >= o) 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. (C) 2019 Elsevier Inc. All rights reserved.