Asymptotic analysis of the non-steady Navier–Stokes equations in a tube structure. I. The case without boundary-layer-in-time

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 2D2D case respectively thin rectangles). The complete asymptotic expansion of the solution is constructed in the case without boundary-layer-in-time. The estimates for the difference of the exact solution and its JJ-th asymptotic approximation is proved. The method of asymptotic partial domain decomposition is formulated and justified for the non-steady Navier–Stokes equations in a tube structure. It gives the asymptotically exact interface conditions of coupling of the 1D and 3D models of the flow. Note that the obtained results hold true for the important in applications case of time periodic flows.