  We demonstrate that superflow past an obstacle is possible in a solid phase
in the one-dimensional Gross-Pitaevskii equation with a finite-range two-body
interaction. The phenomenon we find is analogous to the DC Josephson effect in
superconductors and we deduce the "Josephson relation" between the current and
phase difference of the condensates separated by the obstacle. We also discuss
persistent current and nonclassical rotational inertia in annular container
with a penetrable potential barrier. The phase diagram in the plane of the
current and the interaction strength is given. Our result provides a simple
theoretical example of supersolidity in the presence of an obstacle.
