Momentum transport equation for the fluids using projection-perturbation formalism and onset of turbulence

It is shown that it is possible to derive corrections to the Navier-Stokes equation from the Liouville equation using projection techniques and a perturbation analysis. In the first order the Reynolds equation is obtained, in the second- and third-order corrections to the Navier-Stokes equation are derived raising the possibility of periodic, quasi-periodic and irregular solutions.