Stokes problem

In fluid dynamics, Stokes problem also known as Stokes second problem is a problem of determining the flow created by an oscillating plate, named after Sir George Stokes. This is considered as one of the simplest unsteady problem that have exact solution for the Navier-Stokes equations.

Consider an infinitely long plate which is oscillating with a velocity ${\displaystyle U\cos \omega t}$ in the ${\displaystyle x}$ direction, which is located at ${\displaystyle y=0}$ in an infinite domain of fluid, where ${\displaystyle \omega }$ is the frequency of the oscillations. The incompressible Navier-Stokes equations reduce to

...
Wikipedia