Justification of the asymptotics of solutions of the Navier–Stokes system for low Reynolds numbers

Asymptotics of a generalized solution of the steady-state Navier–Stokes system of equations in a bounded domain $\Omega$ of the three-dimensional space is studied under constraint on the generalized Reynolds number. By methods of functional analysis a theorem about approximation of the exact solution of the homogeneous boundary value problem by partial sums of the found series up to any degree of accuracy in the norm of space $C(\overline\Omega)$ is proved. For the non-steady-state Navier–Stokes system of equations asymptotic approximation in the norm of space $L_2(\Omega)$ is proved.