According to the Landau criterion for superfluidity, a Bose-Einstein
condensate flowing with a group velocity smaller than the sound velocity is
energetically stable to the presence of perturbing potentials. We found that
this is strictly correct only for vanishingly small perturbations. The
superfluid critical velocity strongly depends on the strength and shape of the
defect. We quantitatively study, both numerically and with an approximate
analytical model, the dynamical response of a one-dimensional condensate
flowing against an istantaneously raised spatially periodic defect. We found
that the critical velocity vc decreases by incresing the strength of the
defect V0, up to to a critical value of the defect intensity where the
critical velocity vanishes