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.

arXiv admin note: text overlap with arXiv:1402.1459