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The existence of the velocity potential is a direct consequence from thederivation of the continuity equation from the Schroedinger equation. Thisimplies that the Cole-Hopf transformation is applicable to the Navier-Stokesequation for an incompressible flow and allows reducing the Navier-Stokesequation to the Einstein-Kolmogorov equation, in which the reaction termdepends on the pressure. The solution to the resulting equation, and to theNavier-Stokes equation as well, can then be written in terms of the Green'sfunction of the heat equation and is given in the form of an integral mapping.Such a form of the solution makes bifurcation period doubling possible, i.e.solutions to transition and turbulent flow regimes in spite of the existence ofthe velocity potential.

Exact solutions to the Navier-Stokes equation for an incompressible flow from the interpretation of the Schroedinger wave function