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Analysis and control of some fluid models with variable density

Abstract : In this thesis we study mathematical models concerning some fluid flow problems with variable density. The first chapter is a summary of the entire thesis and focuses on the results obtained, novelty and comparison with the existing literature. In the second chapter we study the local stabilization of the non-homogeneous Navier-Stokes equations in a 2d channel around Poiseuille flow. We design a feedback control of the velocity which acts on the inflow boundary of the domain such that both the fluid velocity and density are stabilized around Poiseuille flow provided the initial density is given by a constant added with a perturbation, such that the perturbation is supported away from the lateral boundary of the channel. In the third chapter we prove the local in time existence of strong solutions for a system coupling the compressible Navier-Stokes equations with an elastic structure located at the boundary of the fluid domain. In the fourth chapter our objective is to study the null controllability of a linearized compressible fluid structure interaction problem in a 2d channel where the structure is elastic and located at the fluid boundary. In this chapter we establish an observability inequality for the linearized fluid structure interaction problem under consideration which is the first step towards the direction of proving the null controllability of the system.
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Submitted on : Tuesday, October 15, 2019 - 10:33:27 AM
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  • HAL Id : tel-01959694, version 2


Sourav Mitra. Analysis and control of some fluid models with variable density. Analysis of PDEs [math.AP]. Université Paul Sabatier - Toulouse III, 2018. English. ⟨NNT : 2018TOU30162⟩. ⟨tel-01959694v2⟩



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