  We address the existence of steady state Green-Keldysh correlation functions
of interacting fermions in mesoscopic systems for both the partitioning and
partition-free scenarios. Under some spectral assumptions on the
non-interacting model and for sufficiently small interaction strength, we show
that the system evolves to a NESS which does not depend on the profile of the
time-dependent coupling strength/bias. For the partitioned setting we also show
that the steady state is independent of the initial state of the inner sample.
Closed formulae for the NESS two-point correlation functions (Green-Keldysh
functions), in the form of a convergent expansion, are derived. In the
partitioning approach, we show that the 0th order term in the interaction
strength of the charge current leads to the Landauer-Buettiker formula, while
the 1st order correction contains the mean-field (Hartree-Fock) results.
