Mathematics – Analysis of PDEs
Scientific paper
2010-02-16
Mathematics
Analysis of PDEs
18 pages
Scientific paper
We study asymptotic dynamics of a coupled system consisting of linearized 3D Navier--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. The main peculiarity of the model is the assumption that the transversal displacements of the plate are negligible relative to in-plane displacements. This kind of models arises in the study of blood flows in large arteries. Our main result states the existence of a compact global attractor of finite dimension. We also show that the corresponding linearized system generates exponentially stable $C_0$-semigroup. We do not assume any kind of mechanical damping in the plate component. Thus our results means that dissipation of the energy in the fluid due to viscosity is sufficient to stabilize the system.
No associations
LandOfFree
A global attractor for a fluid--plate interaction model accounting only for longitudinal deformations of the plate does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with A global attractor for a fluid--plate interaction model accounting only for longitudinal deformations of the plate, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A global attractor for a fluid--plate interaction model accounting only for longitudinal deformations of the plate will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-598586