Towards understanding the algorithms for solving the Navier–Stokes equations

We have explored here the case of three-dimensional non-stationary flows of helical type for the incompressible couple stress fluid with given Bernoulli-function in the whole space (the Cauchy problem).In our presentation, the case of non-stationary helical flows with constant coefficient of proportionality  between velocity and the curl field of flow is investigated.Conditions for the existence of the exact solution for the aforementioned type of flows are obtained, for which non-stationary helical flow with invariant Bernoulli-function is considered satisfying to Laplace equation.The spatial and time-dependent parts of the pressure field of the fluid flow should be determined via Bernoulli-function, if components of the velocity of the flow are already obtained.Analytical and numerical findings have been outlined including outstandung graphical presentations of various types of constructed solution in illuminating dynamical snap-shots which demonstrate developing in time the structural behaviour of topology of the aforepresented solutions.