Special global regular solutions to the Navier-Stokes equations

Ezistence results for global regular solutions to the Navier-Stokes equations, which are close either to two-dimensional or to axially symmetric solutions are presented. Slip boundary conditions are assumed. Moreover, the domains considered are either cylindrical or axially symmetric. Problems with and without inflow-outflow are examined. All proofs can be divided into two steps; (1) long time existence established either by the Leroy Schauder fixed point theorem or by the method of successive approximations; (2) global existence proved by prolongation of a local solution with respcct to time, Bibliography: 32 titles. © 2009 Springer Science+Business Media, Inc.