Oscillations of the total kinematic momentum vector for viscous fluid dynamics in pipes of arbitrary section

We derive the oscillatory exact solutions to Navier–Stokes equations that describe z-invariant viscous fluid flows in a general cylindrical pipe C=D×ℝ1 with section D having an arbitrary geometry and piece-wise smooth boundary ∂D. Exact are presented satisfy no-slip condition at pipe's ∂D×ℝ1 have number of oscillations total kinematic momentum vector on any given interval time [T1,T2]. The stability respect small perturbations infinitely many parameters is proven. new method for generation hierarchy oscillating developed. without external forces (in addition friction pipes's ∂D×ℝ1) derived, which average shift fluid.