  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.
