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Existence de solutions faibles et faible-renormalisées pour des systèmes non linéaires de Boussinesq.

Abstract : The thesis is essentially devoted to prove existence results for some nonlinear partial differential systems of the Boussinesq kind : a Navier-Stokes like motion equation for the velocity and the pressure coupled to an energy conservation equation.
The first chapter gives us a result of existence of a weak-renormalized solution of the Boussinesq system in dimension 2, in the case where F is bounded.
In the chapter 2, we treat the case of more general functions F : F satisfies a growth assumption. We show the existence of solutions for all given initial or for small initial data according to the growth of F.
In the chapter 3, we make a generalization of results of the chapter 2 but without the term of convection.
In the chapter 4, the dissipation energy is not stable in L1(Q) (N = 3), which constrained us to perform a formal transformation on the Boussinesq system. We show the existence of a weak solution of this new system in dimension 3.
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Submitted on : Wednesday, February 27, 2008 - 11:48:14 AM
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Abdelatif Attaoui. Existence de solutions faibles et faible-renormalisées pour des systèmes non linéaires de Boussinesq.. Mathématiques [math]. Université de Rouen, 2007. Français. ⟨tel-00259252⟩

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