Non-stationary helical flows for incompressible 3D Navier-Stokes equations

In fluid mechanics, a lot of authors have been executing their researches to obtain the analytical solutions of Navier-Stokes equations, even for 3D case of compressible gas flow. But there is an essential deficiency of non-stationary solutions indeed.In our derivation, we explore the case of non-stationary helical flow of the Navier-Stokes equations for incompressible fluids at any given initial conditions for velocity fields (it means an open choice for the space part of a solution).Such a non-stationary helical flow is proved to be decreasing exponentially in regard to the time-parameter, the extent of time-dependent exponential component is given by the coefficient of kinematic viscosity, multiplied by the square of the coefficient of proportionality between the vorticity and velocity field.