  We establish pointwise decay estimates for the velocity field of a steady
two-dimensional Stokes flow around a rotating body via a new approach rather
than analysis adopted in the previous literature. The novelty is to analyze the
singular behavior of the constants in these estimates with respect to the
angular velocity of the body, where such singularity is reasonable on account
of the Stokes paradox. We then employ the estimates to identify the asymptotic
structure at infinity of a steady scale-critical Navier-Stokes flow, being
assumed to be small, around a rotating body. It is proved that the leading term
is given by a self-similar Navier-Stokes flow which exhibits a circular profile
and whose coefficient is the torque acting on the body.
