Some theoretical results concerning diphasic fluids in thin films

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 hy...

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Bibliographic Details
Published in:Nonlinear analysis 2015, Vol.116, p.153-179
Main Authors: Bayada, Guy, Chupin, Laurent, Grec, Bérénice
Format: Article
Language:English
Subjects:
Analysis of PDEs
Mathematics
Online Access:Get full text
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Summary: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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2014.12.020