  A recent experiment has demonstrated formation of a supersonic region in a
convergent two-dimensional flow of a condensate of cesium atoms. Theoretical
description of this effect has made use of stationary solutions to the
Gross-Pitaevskii equation with a 3-body dissipative term. Here, we further
develop that description, focusing on a new stationary solution, linear
stability analysis, and properties of the time-dependent "resistive" state.
