Nonstationary Navier-Stokes Equations in Tube Structures

Chapter Nonstationary Navier–Stokes Equations in Tube Structures formulates the nonstationary initial boundary value problem for the Navier–Stokes equations in thin tube structures. The boundary conditions are homogeneous no-slip on the lateral part of the boundary and the given inflow and outflow velocities. The existence and uniqueness of a solution is proved. The asymptotic expansion of the solution is constructed. The error estimates are proved for the difference of the exact solution and its asymptotic approximations. The method of asymptotic partial decomposition of the domain (MAPDD) is described and justified. Numerical experiments confirm the theoretically established error estimates and determine the limitations of the applicability of MAPDD for high Reynolds numbers.