Asymptotic modelling of the fluid flow with a pressure-dependent viscosity

Our goal is to present recent results on the stationary motion of incompressible viscous fluid with a pressure-dependent viscosity. Under general assumptions on the viscosity-pressure relation (satisfied by the Barus formula and other empiric laws), first we discuss the existence and uniqueness of the solution of the corresponding boundary value problem. The main part of the talk is devoted to asymptotic analysis of such system in thin domains naturally appearing in the applications. We address the problems of fluid flow in pipe-like domains and also study the behavior of a lubricant flowing through a narrow gap. In each setting we rigorously derive new asymptotic model describing the effective flow. The key idea is to conveniently transform the governing problem into the Stokes system with small nonlinear perturbation.

This is a joint work with Eduard Marusic-Paloka (University of Zagreb).