On cylindrical symmetric flows through pipe-like domains

We prove existence of cylindrical symmetric solutions to the steady Navier–Stokes equations in bounded pipe -like domains in R3 with the slip boundary conditions. The result is shown for any large flows across the boundary assuming only a geometrical constraint on the shape of the domain which is independent of data. The simply connectedness of the domain is not required. The technique is based on a reformulation of the original problem and delivers us a new type of estimates in the Holder spaces for this class of the solutions.