  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 alpha 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.
