A global attractor for a fluid--plate interaction model
| Autor: | Igor Chueshov, Iryna Ryzhkova |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Physics
Semigroup Applied Mathematics Mathematical analysis Boundary (topology) Physics::Fluid Dynamics Nonlinear system Mathematics - Analysis of PDEs 74F10 35B41 35Q30 74K20 Exponential stability Bounded function Phase space Attractor FOS: Mathematics Displacement (fluid) Analysis Analysis of PDEs (math.AP) |
| Zdroj: | Communications on Pure and Applied Analysis. 12:1635-1656 |
| ISSN: | 1534-0392 |
| DOI: | 10.3934/cpaa.2013.12.1635 |
| Popis: | We study asymptotic dynamics of a coupled system consisting of linearized 3D Navier--Stokes equations in a bounded domain and a classical (nonlinear) elastic plate equation for transversal displacement on a flexible flat part of the boundary. We show that this problem generates a semiflow on appropriate phase space. Our main result states the existence of a compact finite-dimensional global attractor for this semiflow. 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. To achieve the result we first study the corresponding linearized model and show that this linear model generates strongly continuous exponentially stable semigroup. Comment: 29 pages, with Appendix |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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