Compressible Nonlinearly Viscous Fluids: Asymptotic Analysis in a 3D Curved Domain

Abstract

Concerning three-dimensional models, an analytical solution is often impossible and numerical solution can be unduly complicated. Thus, we need to simplify three-dimensional models, when possible, prior to solving the problem. Recently, several lower-dimensional models for dynamics of compressible fluids were rigorously derived from three-dimensional models. We extend the current framework by dealing with nonsteady Navier–Stokes equations for compressible nonlinearly viscous fluids in a deformed three-dimensional domain. The deformation of the domain introduced new difficulties in the asymptotic analysis, because the deformation affects the limit equations in a non-trivial way.