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In this paper we present a method to derive classical solutions of theNavier-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 byimposing certain restrictions on the initial data.

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