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

Abstract

This paper studies exact solutions of the Navier-Stokes equations for a layer between par- allel plates the distance between which increases proportionally to the square root of time. A count- able 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.