An analysis of the Stokes system with pressure dependent viscosity

Eduard Marušič-Paloka, "An analysis of the Stokes system with pressure dependent viscosity", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 46 (2014), pp.123-136In this paper we study the existence and uniqueness of the solution of the Stokes system, describing the flow of a viscous fluid, in case of pressure dependent viscosity

Average of the Navier's Law on the Rapidly Oscillating Boundary

AbstractWe study the flow of Newtonian fluid in a domain with periodically wrinkled boundary with slip (Navier's) boundary condition. The goal of this paper is to replace a microscopic boundary condition, posed on the rough boundary, by some macroscopic boundary condition, posed on the middle surface of the oscillating boundary. Depending on the shape of wrinkles and the friction coefficient we get four different effective models

Derivation of the Reynolds equation for lubrication of a rotating shaft

summary:In this paper, using the asymptotic expansion, we prove that the Reynolds lubrication equation is an approximation of the full Navier–Stokes equations in thin gap between two coaxial cylinders in relative motion. Boundary layer correctors are computed. The error estimate in terms of domain thickness for the asymptotic expansion is given. The corrector for classical Reynolds approximation is computed

Asymptotic Modeling of the Thin Film Flow with a Pressure-Dependent Viscosity

We study the lubrication process with incompressible fluid taking into account the dependence of the viscosity on the pressure. Assuming that the viscosity-pressure relation is given by the well-known Barus law, we derive an effective model using asymptotic analysis with respect to the film thickness. The key idea is to conveniently transform the governing system and then apply two-scale expansion technique

Analysis of the Reynolds Equation for Lubrication in Case of Pressure-Dependent Viscosity

We study the Reynolds equation, describing the ow of a lubricant, in case of pressure-dependent viscosity. First we prove the existence and uniqueness of the solution. Then, we study the asymptotic behavior of the solution in case of periodic roughness via homogenization method. Some interesting nonlocal effects appear due to the nonlinearity