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

الأصل · EN

In this paper, we consider the problem of obtaining rational decay for a particular time-evolving fluid-structure model, the type of which has been considered in Chueshov and Ryzhkova (2013). In particular, this partial differential equation (PDE) system is composed of a three-dimensional Stokes flow which evolves within a three dimensional cavity. Moreover, on a (fixed) portion of the cavity wall, Ω say, a fourth order plate equation is invoked so as to describe the displacements along Ω. Contact between these respective fluid and structure dynamics is established through the boundary interface Ω. Our main result of decay is as follows: The PDE solutions 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 appropriate invocation of a relatively recent resolvent criterion for rational decays for linear strongly continuous semigroups.