  In this article we study the local stabilization of the non-homogeneous
Navier- Stokes equations in a 2d channel around Poiseuille flow. We design a
feedback control of the velocity which acts on the inflow boundary of the
domain such that both the fluid velocity and density are stabilized around
Poiseuille flow provided the initial density is given by a constant added with
a perturbation, such that the perturbation is supported away from the lateral
boundary of the channel. Moreover the feedback control operator we construct
has finite dimensional range.
