Derivation of Reynolds equation for gas lubrication via asymptotic analysis of the compressible Navier-Stokes system

摘要

In this paper we perform asymptotic analysis of the compressible viscous isothermal flow in a periodic domain. We start our analysis by studying the compressible Stokes system in a thin domain of thickness ε?1. As ε tends to zero we obtain the effective behavior of the flow, i.e. the Reynolds model, known from engineering literature, that describes the flow of a gas lubricant. Uniqueness of the solution to Reynolds equations is discussed as well.