  We theoretically investigate how the presence of a reservoir of incoherent
excitations affects the superfluidity properties of resonantly driven polariton
fluids. While in the absence of reservoir the two cases of a defect moving in a
fluid at rest and of a fluid flowing against a static defect are linked by a
formal Galilean transformation, here the reservoir defines a privileged
reference frame attached to the semiconductor structure and causes markedly
different features between the two settings. The consequences on the critical
velocity for superfluidity are highlighted and compared to experiments in
resonantly driven excitons polaritons.
