  We continue our work reported earlier (A. Muriel and M. Dresden, Physica D
101, 299, 1997) to calculate the time evolution of the one-particle
distribution function. An improved operator formalism, heretofore unexplored,
is used for uniform initial data. We then choose a Gaussian pair potential
between particles. With these two conditions, the velocity fields, energy and
pressure are calculated exactly. All stipulations of the Clay Mathematics
Institute for proposed solutions of the 3-D Navier-Stokes Equation are
satisfied by our time evolution equation solution. We then substitute the
results for the velocity fields into the 3-d Navier-Stokes Equation and
calculate the pressure. The results from our time evolution equation and the
prescribed pressure from the Navier-Stokes Equation constitute an exact
solution to the Navier-Stokes Equation. No turbulence is obtained from the
solution. A philosophical discussion of the results, and their meaning for the
problem of turbulence concludes this study.
