English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we consider the problem of obtaining rational decay for aparticular time-evolving fluid-structure model, the type of which has beenconsidered in Chueshov and Ryzhkova (2013). In particular, this partialdifferential equation (PDE) system is composed of a three-dimensional Stokesflow which evolves within a three dimensional cavity. Moreover, on a (fixed)portion of the cavity wall, $\Omega$ say, a fourth order plate equation isinvoked so as to describe the displacements along $\Omega$. Contact betweenthese respective fluid and structure dynamics is established through theboundary interface $\Omega$. Our main result of decay is as follows: The PDEsolutions of this fluid-structure PDE, corresponding to smooth initial data,decay at the rate of $O(1/t)$. Our method of proof hinges upon the appropriateinvocation of a relatively recent resolvent criterion for rational decays forlinear strongly continuous semigroups.

Spectral analysis and rational decay rates of strong solutions to a fluid-structure PDE system