Time-dependent solutions of the Navier-Stokes equations

An attempt is made to solve the Navier-Stokes equations for the incompressible laminar flow around an infinite porous plate in unsteady motion with a time-dependent velocity. The Laplace transform applied to the coordinate normal to the wall is used to transform the Navier-Stokes equations into integral equations, and finds exact solutions for them in the case of time-dependent velocity of suction through the plate.