The Navier-Stokes Existence and Smoothness Poser in $\mathbb{R}^n$

Abstract: In this paper we describe a method to derive solutions of the incompressible Navier- Stokes system of equations for non-stationary initial value problems in $\mathbb{R}^n$. 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 $\mathbb{R}^3$ provides important insights into the ostensible phenomenon of the blowup time.