The new effect of oscillations of the total kinematic momentum vector of viscous fluid

Abstract

The new effect of oscillations of the total kinematic momentum is discovered for dynamics of viscous fluid in cylindrically symmetric pipe with no-slip condition at the boundary. Stability of oscillations with respect to small perturbations of infinite-dimensional family of parameters is proven. Exact solutions to the three-dimensional (3-D) Navier - Stokes equations without external forces (besides the friction forces at the pipe's boundary) are derived possessing any number of oscillations of average angular velocity and any number of oscillations of average shift of viscous fluid satisfying the no-slip boundary condition.