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

Guy Bayada (1) , Laurent Chupin (1) , Bérénice Grec (1)

1 ICJ - Institut Camille Jordan

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 non-linear non local Hertz law. The viscosity is supposed to depend non-linearly 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.

Domaines: Equations aux dérivées partielles [math.AP]

Guy Bayada, Laurent Chupin, Bérénice Grec. An unconditional existence result for elastohydrodynamic piezoviscous lubrication problems with Elrod-Adams model of cavitation. Differential and integral equations, 2008, 21 (1-2), pp.41-62. ⟨hal-00777512⟩