Special global regular solutions to the Navier–Stokes equations

We present the existence results of global regular solutions to the Navier–Stokes equations which are close either to two-dimensional or to axially-symmetric solutions. We assume the slip-boundary conditions. Moreover, the considered domains are either cylindrical or axially symmetric. We examine problems with and without inflow-outflow. All proofs can be divided into two steps: 1. long time existence by either the Leray–Schauder fixed point theorem or the method of successive approximations, 2. global existence by prolongation of the local solution with respect to time. Bibl. – 32 titles.