Stochastic dynamics in a fluid--plate interaction modelwith the only longitudinal deformations of the plate
Igor Dmitrievich Chueshov, Björn Schmalfuß · Discrete and Continuous Dynamical Systems - B · 2015
We consider a stochastically perturbed coupled system consisting of linearized 3DNavier--Stokes equations in a bounded domain and the classical (nonlinear)elastic plate equation for in-plane motions on a flexible flat part of the boundary. This kind of models arises inthe study of blood flows in large arteries.Our main result states the existence of a random pullback attractorof finite fractal dimension. Our argument is based on some modification of the method ofquasi-stability estimates recently developed for deterministic systems.