The problem of an unsteady axisymmetric expansion of a monatomic gas into a vacuum is considered in the limit of small source Knudsen number. It is shown that a solution of the Boltzmann equation for Maxwell molecules valid for large time can be constructed, which matches with the known equilibrium solution for an inviscid expansion of a fixed mass of gas into a vacuum provided that the region near the zero density front is excluded. This solution is formally the same as that obtained for the similar problem of steady spherical expansion into a vacuum—the variations along each particle path of the unsteady flow being the same as that in the steady flow.

Near the front, the expansion procedure breaks down and the equations require a different scaling. A modified form of the Boltzmann equation is obtained which leads to a corresponding set of moment equations. Unfortunately, the set of moment equations is no longer closed and no essential simplification has been made.