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Existence results for flows of slightly compressible viscoelastic fluids in a bounded domain with corners

Abstract : Steady flows of slightly compressible viscoelastic fluids of Oldroyd's type with zero boundary conditions are considered on a bounded two-dimensional domain with an isolated corner point. We prove the existence and the uniqueness of the solution for small data in weighted Sobolev spaces Vξk, where the index ξ characterizes the power growth of the solution near the angular point. The proof follows from an analysis of a linearized problem through the fixed point theory. We use a method of decomposition for such linearized equations: the velocity field u is split into a non-homogeneous incompressible part v and a compressible part ∇φ.
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https://hal-upec-upem.archives-ouvertes.fr/hal-00803959
Contributor : Colette Guillope <>
Submitted on : Sunday, March 24, 2013 - 10:51:41 AM
Last modification on : Thursday, March 19, 2020 - 12:26:03 PM

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Colette Guillopé, Zaynab Salloum, Raafat Talhouk. Existence results for flows of slightly compressible viscoelastic fluids in a bounded domain with corners. Analysis and Applications, World Scientific Publishing, 2012, 10 (4), pp.381-411. ⟨10.1142/S0219530512500194⟩. ⟨hal-00803959⟩

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