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.