Unsteady interaction of a viscous fluid with an elastic shell modeled by full von Karman equations
| Autor: | Iryna Ryzhkova, Igor Chueshov |
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| Rok vydání: | 2013 |
| Předmět: |
Applied Mathematics
media_common.quotation_subject Mathematical analysis Shell (structure) FOS: Physical sciences Mathematical Physics (math-ph) Moment of inertia Viscous liquid Inertia Nonlinear system Mathematics - Analysis of PDEs 74F10 35B41 35Q30 74K20 Phase space Fluid–structure interaction Attractor FOS: Mathematics Mathematical Physics Analysis Analysis of PDEs (math.AP) media_common Mathematics |
| Zdroj: | Journal of Differential Equations. 254:1833-1862 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2012.11.006 |
| Popis: | We study well-posedness and asymptotic dynamics of a coupled system consisting of linearized 3D Navier–Stokes equations in a bounded domain and a classical (nonlinear) full von Karman shallow shell equation that accounts for both transversal and lateral displacements on a flexible part of the boundary. We also take into account rotational inertia of filaments of the shell. Our main result shows that the problem generates a semiflow in an appropriate phase space. The regularity provided by viscous dissipation in the fluid allows us to consider simultaneously both cases of presence inertia in the lateral displacements and its absence. Our second result states the existence of a compact global attractor for this semiflow in the case of presence of (rotational) damping in the transversal component and a particular structure of external forces. |
| Databáze: | OpenAIRE |
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