  In this paper, we construct the axisymmetric weak solutions to the 3D
isothermal stationary compressible Navier-Stokes equations on the domain D,
where the heat ratio equal 1 and the external force g satisfies certain
cancellation conditions. We first establish the compactness assertion of the
approximation solutions by assuming the total mass of the fluid is finite, then
we exclude the trivial solution via imposing another type of restrictions on
the density. To deal with the singularities near the symmetric axis and at the
far field, we will derive proper weighted estimates of the L2-norm of the
velocity field on the unbounded domain D, which belongs to the critical case of
the Sobolev's inequality.
