Viscoelastic fluids in thin domains: a mathematical proof

Guy Bayada (1, 2) , Laurent Chupin (1) , Bérénice Grec (1)

1 ICJ - Institut Camille Jordan
2 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]

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 sytem towards the asymptotic model.

Domaines: Equations aux dérivées partielles [math.AP]

Guy Bayada, Laurent Chupin, Bérénice Grec. Viscoelastic fluids in thin domains: a mathematical proof. Asymptotic Analysis, 2009, 64 (3-4), pp.185-211. ⟨10.3233/ASY-2009-0940⟩. ⟨hal-00340253⟩