Differential and Integral Equations

An unconditional existence result for elastohydrodynamic piezoviscous lubrication problems with Elrod-Adams model of cavitation

Guy Bayada, Laurent Chupin, and Bérénice Grec

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Abstract

An unconditional existence result of a solution for a steady fluid-structure problem is stated. More precisely, we consider an incompressible fluid in a thin film, ruled by the Reynolds equation coupled with a surface deformation modelled by a nonlinear non local Hertz law. The viscosity is supposed to depend nonlinearly on the fluid pressure. Due to the apparition of a mushy region, the two-phase flow satisfies a free boundary problem defined by a pressure-saturation model. Such a problem has been studied with simpler free boundaries models (variational inequality), or with boundary conditions imposing small data assumptions. We show that up to a realistic hypothesis on the asymptotic pressure-viscosity behaviour it is possible to obtain an unconditional solution of the problem.

Article information

Source
Differential Integral Equations, Volume 21, Number 1-2 (2008), 41-62.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039058

Mathematical Reviews number (MathSciNet)
MR2479661

Zentralblatt MATH identifier
1224.35436

Subjects
Primary: 35Q35: PDEs in connection with fluid mechanics
Secondary: 74K35: Thin films 76D08: Lubrication theory

Citation

Bayada, Guy; Chupin, Laurent; Grec, Bérénice. An unconditional existence result for elastohydrodynamic piezoviscous lubrication problems with Elrod-Adams model of cavitation. Differential Integral Equations 21 (2008), no. 1-2, 41--62. https://projecteuclid.org/euclid.die/1356039058


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