Well-Posedness and Long Time Behavior for a Class of Fluid-Plate Interaction Models - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2013

Well-Posedness and Long Time Behavior for a Class of Fluid-Plate Interaction Models

Igor Chueshov
  • Function : Author
  • PersonId : 850365
Iryna Ryzhkova
  • Function : Author
  • PersonId : 986423

Abstract

We deal with well-posedness and asymptotic dynamics of a class of coupled systems consisting of linearized 3D Navier–Stokes equations 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 transversal 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 additional smoothness. We do not assume any kind of mechanical damping in the plate component in the case of models (a) and (b). Thus our results means that dissipation of the energy in the fluid due to viscosity is sufficient to stabilize the system in the latter cases.
Fichier principal
Vignette du fichier
978-3-642-36062-6_33_Chapter.pdf (4 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01347553 , version 1 (21-07-2016)

Licence

Attribution

Identifiers

Cite

Igor Chueshov, Iryna Ryzhkova. Well-Posedness and Long Time Behavior for a Class of Fluid-Plate Interaction Models. 25th System Modeling and Optimization (CSMO), Sep 2011, Berlin, Germany. pp.328-337, ⟨10.1007/978-3-642-36062-6_33⟩. ⟨hal-01347553⟩
57 View
71 Download

Altmetric

Share

Gmail Facebook X LinkedIn More