Asymptotic analysis of the non-steady Navier–Stokes equations in a tube structure. II. General case. (September 2015) - Panasenko, Grigory; Pileckas, Konstantin
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 2 D 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 J th asymptotic approximation are proved.