An Exact Simple Solution of the Compressible Navier-Stokes Equation*

We display a simple exact solution of the compressible Navier-Stokes equation without an external field. The field velocities and density are:
vx = no vxo exp[-a{(x-vxo t)^2+(y-vyo t)^2+(z-vzo t)^2}]
vy = no vyo exp[-a{(x-vxo t)^2+(y-vyo t)^2+(z-vzo t)^2}]
vz = no vzo exp[-a{(x-vxo t)^2+(y-vyo t)^2+(z-vzo t)^2}]
n = no exp[-a{(x-vxo t)^2+(y-vyo t)^2+(z-vzo t)^2}]
where all variables are defined and explained in A. Muriel, Results in Physics 6, 461 (2016) or ResearchGate, amadormuriel@gmail.com. The pressure tensors are calculable from the above field velocities using the Navier-Stokes equation itself. The density, the field velocities and the derivable pressure tensors constitute the simplest exact solution to date of the Navier-Stokes equation. We invite readers to check the self-consistency of the solution. The origin of this solution, as well as others. will be explained and illustrated. Surprisingly, this simple solution meets all stipulations of the problem definition by the Clay Institute of Mathematics. This solution is valid for a compressible fluid instead of an incompressible fluid required by the Institute.