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Theses

Comportement asymptotique de problèmes posés dans des cylindres. Problèmes d'unicité pour des systèmes de Boussinesq

Abstract : The thesis is divided in two independent parts.
In the first part, we investigate the asymptotic behaviour of elliptic and parabolic problems with $L^1+W^{-1,p'}$ data (respectively with $L^1+L^p(0,T;W^{-1,p'})$ data in the parabolic case), in domains becoming unbounded. Using the framework of renormalized solutions and the regularity results of the solutions for such data, we prove, under structural conditions on space variables, convergence results in spaces containing the solutions.
In the second part, in the $2$-dimensional case, we study Boussinesq type systems. These systems derive from fluid mechanics models and couple incompressible Navier-Stokes equations and heat equation. We focus our attention on studying the uniqueness of the solution, which is intricate because of the very nonlinear coupling of the equations. We consider weak solutions for the Navier-Stokes equations and renormalized solutions are used for the heat equation. We state regularity results for these equations and then we prove few existence and uniqueness results of the solution of the system for small data.
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https://tel.archives-ouvertes.fr/tel-00199798
Contributor : Nicolas Bruyere <>
Submitted on : Wednesday, December 19, 2007 - 3:53:55 PM
Last modification on : Tuesday, February 5, 2019 - 11:44:10 AM
Long-term archiving on: : Monday, April 12, 2010 - 8:33:25 AM

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  • HAL Id : tel-00199798, version 1

Citation

Nicolas Bruyere. Comportement asymptotique de problèmes posés dans des cylindres. Problèmes d'unicité pour des systèmes de Boussinesq. Mathématiques [math]. Université de Rouen, 2007. Français. ⟨tel-00199798⟩

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