Some theoretical results concerning diphasic fluids in thin films

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]

We are interested in a model for diphasic fluids in thin flows taking into account both the hydrodynamical and the chemical effects at the interface between the two fluids. A limit problem in "thin films" is introduced heuristically. It is a system coupling the Reynolds equation and the hydrodynamical Cahn-Hilliard equation. We study the mathematical properties of this system, and prove an existence result under some smallness condition on the data.

Domaines: Equations aux dérivées partielles [math.AP]

Guy Bayada, Laurent Chupin, Bérénice Grec. Some theoretical results concerning diphasic fluids in thin films. 2009. ⟨hal-00383732v1⟩