  Landau solutions are special solutions to the stationary incompressible
Navier-Stokes equations in the three dimensional space excluding the origin.
They are self-similar and axisymmetric with no swirl. In fact, any self-similar
smooth solution must be a Landau solution. In the effort of extending this
result to the one for the solution class with the pointwise scale-invariant
bound $|u(x)|\leq C_0|x|^{-1}$ for some $C_0>0$, we consider axisymmetric
discretely self-similar solutions, and investigate the existence of such
solution curve emanating from some Landau solution. We prove that the inclusion
of the swirl component does not enhance the bifurcation and present numerical
evidence of no bifurcation.
