Asymptotic analysis of the linearized Navier–Stokes equations in a general 2D domain

Abstract

We continue our study of the asymptotic behavior of the Navier–Stokes equations linearized around the rest state as viscostiy ε approaches zero. We study the convergence as ε→0 to the inviscid type equations. Suitable correctors are obtained which resolve the boundary layer and we obtain convergence results valid up to the boundary. Explicit asymptotic expansion formulas are given which display the boundary layer phenomena. We improve our previous by treating here the general smooth bounded domain in R² instead of two-dimensional channels. Curvilinear coordinates are used to resolve the complex geometry.