  In this paper, we study the Vlasov-Navier-Stokes system in a 2D pipe with
partially absorbing boundary conditions. We show the existence of stationary
states for this system near small Poiseuille flows for the fluid phase, for
which the kinetic phase is not trivial. We prove the asymptotic stability of
these states with respect to appropriately compactly supported perturbations.
The analysis relies on geometric control conditions which help to avoid any
concentration phenomenon for the kinetic phase.
