  The flow of a uniform Bose gas at speeds greater than the Landau critical
velocity, v_c, does not necessarily destroy superfluidity, but rather need only
lead to a decrease of the superfluid mass density, {\rho}_s. Analyzing a weakly
interacting Bose gas with a finite range interparticle interaction that leads
to a Landau critical velocity at non-zero quasiparticle momentum, we explicitly
construct the (non-uniform) condensate for fluid flow faster than v_c and
calculate the accompanying decrease in {\rho}_s. We briefly comment on the
relation of the physics to other problems in superfluids, e.g., solitons, and
vortices in Bose-Einstein condensates, and critical currents in
superconductors.
