2013/12/17 by George Avalos, Avalos, George, Francesca Bucci +1
Computer Science · Engineering · Mathematics · #35B35 #35M33 #76D07 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP #msc:35B35 #msc:35M33 #msc:76D07
paper · pdf · doi:10.48550/arxiv.1312.4812
19 pages, 1 figure
arxiv created 2013/12/17 · openalex publication_date 2013/12/17 · arxiv updated 2013/12/18 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
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.