Asymptotic behaviour of the Stokes problem in cylinders

We study the asymptotics of the Stokes problem in cylinders becoming unbounded in the direction of their axis. We consider

especially the case where the forces are independent of the axis coordinate and the case where they are periodic along the axis, but the same

techniques also work in a more general framework.

We present in detail the case of constant forces (in the axial direction) since it is probably the most interesting for applications and also

because it allows to present the main ideas in the simplest way. Then we briefly present the case of periodic forces on general periodic domains. Finally, we give a result under much more general assumptions on the applied forces.