An unconditional existence result for elastohydrodynamic piezoviscous lubrication problems with Elrod-Adams model of cavitation. (English) Zbl 1224.35436

Summary: An unconditional existence result of a solution for a steady fluid-structure problem is stated. More precisely, 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 is considered. 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. It is shown that up to a realistic hypothesis on the asymptotic pressure-viscosity behaviour it is possible to obtain an unconditional solution of the problem.


35R35 Free boundary problems for PDEs
35B45 A priori estimates in context of PDEs
35B65 Smoothness and regularity of solutions to PDEs
74K35 Thin films
76D08 Lubrication theory