  We examine the superfluid properties of a 1D Bose gas in a ring trap based on
the model of Lieb and Liniger. While the 1D Bose gas has nonclassical
rotational inertia and exhibits quantization of velocities, the metastability
of currents depends sensitively on the strength of interactions in the gas: the
stronger the interactions, the faster the current decays. It is shown that the
Landau critical velocity is zero in the thermodynamic limit due to the first
supercurrent state, which has zero energy and finite probability of excitation.
We calculate the energy dissipation rate of ring currents in the presence of
weak defects, which should be observable on experimental time scales.
