  We consider the problem of asymptotic stability and linear inviscid damping
for perturbations of a point vortex and similar degenerate circular flows.
Here, key challenges include the lack of strict monotonicity and the necessity
of working in weighted Sobolev spaces whose weights degenerate as the radius
tends to zero or infinity. Prototypical examples are given by circular flows
with power law singularities or zeros as $r\downarrow 0$ or $r \uparrow
\infty$.
