Exact unsteady solutions of the Navier-Stokes equation

Unsteady solutions of the Naviear-Stokes equation which are not limited to boundary regions, which take convective forces into account, and which can be expressed as elementary functions are developed. The case of an incompressible Newtonian fluid between two plane surfaces of infinite extension, moving normal to their plane according to two time laws, is considered. Two types of similarity solutions of the resulting Navier-Stokes equation are discussed. It is considered remarkable that the flow time laws can be both monotonically rising and monotonically falling, so that the solutions apply whether the walls are converging or diverging.