Calculation of Reynolds equation for the generalized non-Newtonian fluids and its asymptotic behavior in a thin domain

Abstract

Three-dimensional boundary-value problem describing a generalized non-Newtonian fluid with nonlinear Tresca friction type in a thin domain Ω ε {\Omega^{\varepsilon}} are considered. We study the asymptotic behavior when one dimension of the fluid domain tends to zero. We prove some weak convergence of the velocity and the pressure of the fluid. Then the limit problem in two-dimensional domain and the specific Reynolds equation are obtained.