We deal with well-posedness and asymptotic dynamics of a class of coupled systems consisting of linearized 3D Navier-Stokes equa- tions in a bounded domain and a classical (nonlinear) elastic plate/shell equation. We consider three models for plate/shell oscillations: (a) the model which accounts for transversal displacement of a flexible flat part of the boundary only, (b) the model for in-plane motions of a flexible flat part of the boundary, (c) the model which accounts for both transver- sal and longitudinal displacements. For all three cases we present well- posedness results and prove existence of a compact global attractor. In the first two cases the attractor is of finite dimension and possesses ad- ditional smoothness. We do not assume any kind of mechanical damping in the plate component in the case of models (a) and (b). Thus our re- sults means that dissipation of the energy in the fluid due to viscosity is sufficient to stabilize the system in the latter cases.
['Igor Chueshov', 'Iryna Ryzhkova']
Well-Posedness and Long Time Behavior for a Class of Fluid-Plate Interaction Models