Existence and uniqueness results for compressible Reynolds equation with slip boundary conditions

ABSTRACT

In this paper a one dimensional system describing the behaviour of a thin film flow (lubrication assumption) is analysed for various non linear slip conditions on the solid surface including Tresca shear limited models. So far, existence results for such problems require an incompressibility assumption. In the present work, this assumption is removed, allowing cavitation to be taken into account. The possibility of considering such models including simultaneously cavitation and slip/no-slip conditions is of practical importance as this corresponds to the actual trend in lubrication engineering.

COMMUNICATED BY:

• Brahim Amaziane

Keywords:

• Hydrodynamic lubrication
• slip condition
• shear limited model
• cavitation
• variational inequality

2010 Mathematics Subject Classifications:

• 35R35
• 76N10

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Centre National pour la Recherche Scientifique et Technique (CNRST) Project URAC 01 Morocco.