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Some results of existence, controllability and stabilization for fluid - structure coupled systems

Abstract : In this thesis, we are interested in the study of fluid-structure systems. These systems may model blood flows in large vessels. The velocity and the pressure of the blood are sdescribed by the incompressible Navier-Stokes equations and the displacement of the mobile part of the boundary satisfies a beam/plate equation (it depends on the dimension of the model). In the fist part, we prove the exitence and uniqueness of strong solutions to two systems (they correspond with the zero or nonzero value of a certain paramter) in two and three dimensions. More precisely, we prove the following alternative. We have either global existence for small initial data or local existence for any initial data. In the second part, we study on one hand the null controllability of a system coupling the Navier-Stokes equations with a finite dimensional beam equation for small initial data in two dimensions. On the other hand, we prove the stabilzation (for any decay rate) of a system coupling the Navier-Stokes equations with two beam equations with two controls in the periodic setting for small initial data. In this case, the controls are of finite dimension.
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Contributor : Julien Lequeurre <>
Submitted on : Wednesday, April 4, 2012 - 10:19:42 AM
Last modification on : Thursday, March 5, 2020 - 5:57:03 PM
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  • HAL Id : tel-00685107, version 1

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Julien Lequeurre. Some results of existence, controllability and stabilization for fluid - structure coupled systems. Analysis of PDEs [math.AP]. Université Paul Sabatier - Toulouse III, 2011. English. ⟨tel-00685107⟩

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