The Navier-Stokes existence and smoothness poser in Rn

In this paper we describe a method to derive solutions of the Navier-Stokes equations for non-stationary initial value problems in Rn. We show that for a given smooth solenoidal initial velocity vector field there exist smooth spatially periodic solutions of pressure and velocity in $\mathbb{R}^n$. An illustrative example in $\mathbb{R}^3$ is presented.