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Theses

Quelques problèmes aux limites pour des équations de Navier-Stokes compressibles et isentropiques

Abstract : In this thesis, we deal with the problem of existence of weak solutions to the compressible and isentropic Navier-Stokes equations. This study was motivated by the works of P.L. Lions in which the author solves this problem when the region filled with the fluid is smooth and under assumptions for the adiabatic constant which are not always satisfactory from the physical point of view. A method to weaken these assumptions was suggested recently by E. Feireisl and it was applied to the equations of evolution. In the steady case, we prove existence of a renormalized bounded energy weak solution in bounded regions with Lipschitz boundary and in some cases, we improve the assumptions for the adiabatic constant. We also study flows in unbounded regions with several outlets at infinity. In this case, we define bounded energy weak solutions letting appear in the energy inequality the notion of flux through each outlet and the notion of pressure drop between the outlets. We prove existence of such solutions when the outlets are conical while for cylindrical outlets, we show a non-existence result. In the unsteady case, we prove existence of weak solutions for a problem with inflow-outflow boundary conditions in a bounded region with a special shape. This part of this thesis is inspired by the work of E. Feireisl about the shape optimization in a viscous compressible flow.
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https://tel.archives-ouvertes.fr/tel-00004012
Contributor : Sébastien Novo <>
Submitted on : Wednesday, December 17, 2003 - 4:50:16 PM
Last modification on : Thursday, March 5, 2020 - 4:23:04 PM
Long-term archiving on: : Friday, April 2, 2010 - 7:53:58 PM

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Sébastien Novo. Quelques problèmes aux limites pour des équations de Navier-Stokes compressibles et isentropiques. Mathématiques [math]. Université du Sud Toulon Var, 2002. Français. ⟨tel-00004012⟩

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