Viscoelastic fluids in thin domains: A mathematical proof

Article type: Research Article

Authors: Bayada, Guy^; | Chupin, Laurent | Grec, Bérénice^;

Affiliations: INSA-Lyon, Institut Camille Jordan, CNRS UMR 5208 | INSA-Lyon, LAMCOS, CNRS UMR 5259 | Ecole Centrale de Lyon, Institut Camille Jordan, CNRS UMR 5208

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Abstract: The present paper deals with non-Newtonian viscoelastic flows of Oldroyd-B type in thin domains. Such geometries arise for example in the context of lubrication. More precisely, we justify rigorously the asymptotic model obtained heuristically by proving the mathematical convergence of the Navier–Stokes/Oldroyd-B system towards the asymptotic model.

Keywords: viscoelastic fluids, thin film, Oldroyd model, lubrication flow, asymptotic analysis

DOI: 10.3233/ASY-2009-0940

Journal: Asymptotic Analysis, vol. 64, no. 3-4, pp. 185-211, 2009