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Theses

Sur des problèmes de lubrification stationnaires et instationnaires non isothermes

Abstract : The objective of this thesis is to study some elliptic and parabolic problems of the non-Newtonian flow of an incompressible and non isothermal fluid governed by partial differential equation of Stokes with Tresca’s condition on a part of the boundary when the fluid viscosity depends on temperature and also on the modulus of strain rate tensor and the velocity of the fluid. In the first chapter, we did a general introduction. In the second chapter, we consider the coupling between the Stokes systemand the heat equation in steady state. We prove the existence of a solution of the variational inequality describing the Stokes system when the fluid viscosity depends on temperature and also on the modulus of strain rate tensor and the velocity of the fluid of a given temperature by using the monotony methods for the velocity and De Rham’s theorem for the pressure. We study the existence and uniqueness of the temperature solution of the heat equation with L1 (Ω) term to the second member when the fluid viscosity depends on temperature and also on the modulus of strain rate tensor and the velocity of the fluid. We show the existence of a solution of the coupled variational problem when the fluid viscosity depends on temperature and also on the modulus of strain rate tensor by using Schauder fixed point theorem. In the third and the fourth chapter, we treate the existence and uniqueness of a solution of the Stokes system in unsteady state when the fluid viscosity depends only on temperature and on the modulus of strain rate tensor in the cases p = 2, p > 2 and 6 5 < p < 2 by using the notion of semigroup and monotony methods for the velocity and De Rham’s theorem for the pressure. However, when the fluid viscosity depends also on the velocity of the fluid we obtain only the existence by Schauder fixed point theorem
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Hanene Debbiche. Sur des problèmes de lubrification stationnaires et instationnaires non isothermes. Physique mathématique [math-ph]. Université de Lyon, 2016. Français. ⟨NNT : 2016LYSES027⟩. ⟨tel-01845063⟩

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