Existence of Weak Solutions for the Three-Dimensional Motion of an Elastic Structure in an Incompressible Fluid |
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Authors: | Muriel Boulakia |
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Affiliation: | (1) Laboratoire de Mathématiques Appliquées, Université de Versailles–St-Quentin, 45 avenue des Etats Unis, 78035 Versailles Cedex, France |
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Abstract: | We study here the three-dimensional motion of an elastic structure immersed in an incompressible viscous fluid. The structure
and the fluid are contained in a fixed bounded connected set Ω. We show the existence of a weak solution for regularized elastic
deformations as long as elastic deformations are not too important (in order to avoid interpenetration and preserve orientation
on the structure) and no collisions between the structure and the boundary occur. As the structure moves freely in the fluid,
it seems natural (and it corresponds to many physical applications) to consider that its rigid motion (translation and rotation)
may be large.
The existence result presented here has been announced in 4]. Some improvements have been provided on the model: the model
considered in 4] is a simplified model where the structure motion is modelled by decoupled and linear equations for the translation,
the rotation and the purely elastic displacement. In what follows, we consider on the structure a model which represents the
motion of a structure with large rigid displacements and small elastic perturbations. This model, introduced by 15] for a
structure alone, leads to coupled and nonlinear equations for the translation, the rotation and the elastic displacement. |
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Keywords: | 74F10 35Q30 37N15 76D03 |
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