Stability of superflow

The stability of uncharged superflow is studied within the Ginzburg-Landau theory. The linear-stability problem for flow in the presence of a flat wall is solved analytically. We prove that the critical velocity is not modified from its value for homogeneous superflow if the order parameter is required to vanish at the wall. We further show that surface roughness on the scale of the coherence length does have a strong effect on the stability of the flow. The critical velocity in the vicinity of a two-dimensional surface ``bump'' is well described by a power law for the parameter values considered.