Classical analytic solutions of the non-stationary Navier-Stokes equation in two, three and higher dimensions

In this paper we present a method to derive classical solutions of the Navier-Stokes equations for non-stationary initial value problems in domain ${\mathbb{R}}^n$ ($n=2,3$ or higher). Exact solutions in ${\mathbb{R}}^2$ and ${\mathbb{R}}^3$ in the presence of an externally specified force are obtained by imposing certain restrictions on the initial data.