The problem of the steady axially symmetric expansion of a monatomic gas from an orifice into a vacuum is considered. The reservoir conditions are such that the local Knudsen number is initially small. It is noted that the near continuum solution, valid near the orifice, is not uniformly valid far downstream where the local mean free path may be comparable with some characteristic length. A valid solution of Boltzmann's equation, for Maxwell molecules, is deduced for this far field core region. Near the gas‐vacuum front, predicted by the equilibrium solution, this expansion procedure also breaks down. It is shown that a further scaling of the variables in Boltzmann's equation, consistent with this limit, can be found and the corresponding moment equations deduced. However, in contrast to the behavior in the core, these equations no longer form a closed set.