Some theoretical results concerning diphasic fluids in thin films

We are interested in a model for diphasic uids in thin ows taking into ac- count both the hydrodynamical and the chemical eects at the interface between the two uids. A limit problem in \thin lms" 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 small- ness condition on the data.