Exact solution of the Navier-Stokes equations in a fluid layer between the moving parallel plates

This paper studies exact solutions of the Navier-Stokes equations for a layer between parallel plates the distance between which increases proportionally to the square root of time. A countable set of exact solutions and their derived countable set of continuous families of exact solutions are obtained. It is shown that certain intervals of the Reynolds parameter have two solutions and some of them one solution.