Asymptotic analysis of the non-steady Navier–Stokes equations in a tube structure. II. General case

Abstract

The non-steady Navier–Stokes equations with Dirichlet boundary conditions are considered in thin tube structures. These domains are connected finite unions of thin finite cylinders (in the 2D case respectively thin rectangles). The complete asymptotic expansion of the solution is constructed. It contains a regular part and three types of the boundary layer correctors: “in-space”, “in-time” and “in-space-and-in-time”. The estimates for the difference of the exact solution and its Jth asymptotic approximation are proved.