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Application of very weak formulation on homogenization of boundary value problems in porous media

Eduard Marušić-Paloka — 2021

Czechoslovak Mathematical Journal

The goal of this paper is to present a different approach to the homogenization of the Dirichlet boundary value problem in porous medium. Unlike the standard energy method or the method of two-scale convergence, this approach is not based on the weak formulation of the problem but on the very weak formulation. To illustrate the method and its advantages we treat the stationary, incompressible Navier-Stokes system with the non-homogeneous Dirichlet boundary condition in periodic porous medium. The...

Derivation of the Reynolds equation for lubrication of a rotating shaft

Antonija Duvnjak;  Eduard Marušić-Paloka — 2000

Archivum Mathematicum

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.

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