Lagrangian controllability at low Reynolds number

In this paper, we establish a result of Lagrangian controllability for a fluid at low Reynolds number, driven by the stationary Stokes equation. This amounts to the possibility of displacing a part of a fluid from one zone to another by suitably using a boundary control. This relies on a weak variant of the Runge–Walsh’s theorem (on approximation of harmonic functions) concerning the Stokes equation. We give two variants of this result, one of which we believe to be better adapted to numerical simulations