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.
Citation
Guy Bayada. Laurent Chupin. Bérénice Grec. "An unconditional existence result for elastohydrodynamic piezoviscous lubrication problems with Elrod-Adams model of cavitation." Differential Integral Equations 21 (1-2) 41 - 62, 2008. https://doi.org/10.57262/die/1356039058
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