On some new types of non-stationary analytical solutions of Navier-Stokes equations

We consider the Navier-Stokes equations for the axis-symmetrical rotational motions of viscous incompressible fluid. We look for the solutions for these equations in the form of specific expressions, leading to the systems convenient for study. The analysis of the obtained systems allows to find some new types of non-stationary analytical solutions of Navier-Stokes equations. The properties of the obtained solutions are discussed. Also we consider peculiarities some of them posses for large Reynolds numbers, when turbulence may arise, and for cases when areas of cavity are formed.