Étude mathématique d’écoulements de fluides viscoélastiques dans des domaines singuliers

Abstract : In this PHD thesis, we study three problems for viscoelastic flows of Oldroyd type. First, we study steady flows of slightly compressible in a bounded domain with non-zero velocities on the boundary ; the pressure and the extra-stress tensor are prescribed on the part of the boundary corresponding to entering velocity. This causes a weak singularity in the solution at the junction of incoming and outgoing flows. We also study the problem of steady flows of slightly compressible fluids with zero boundary conditions in a domain with an isolated corner point. Using a method of fixed point (first and second problems) and a Helmoltz decomposition (second problem), we show some results of existence and uniqueness of solutions. In the last part, we study the case of a non-steady flow : we show some results of local and of global existence, with sufficiently small initial data, for compressible flows. The zero-Mach number limit is also established
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General Mathematics [math.GM]. Université Paris-Est, 2008. French. <NNT : 2008PEST0017>


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Zaynab Salloum. Étude mathématique d’écoulements de fluides viscoélastiques dans des domaines singuliers. General Mathematics [math.GM]. Université Paris-Est, 2008. French. <NNT : 2008PEST0017>. <tel-00461675>

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