  I consider a Corbino-geometry SNS (superconducting-normal-superconducting)
Josephson weak link in a thin superconducting film, in which current enters at
the origin, flows outward, passes through an annular Josephson weak link, and
leaves radially. In contrast to sandwich-type annular Josephson junctions, in
which the gauge-invariant phase difference obeys the sine-Gordon equation, here
the gauge-invariant phase difference obeys an integral equation. I present
exact solutions for the gauge-invariant phase difference across the weak link
when it contains an integral number N of Josephson vortices and the current is
zero. I then study the dynamics when a current is applied, and I derive the
effective resistance and the viscous drag coefficient; I compare these results
with those in sandwich-type junctions. I also calculate the critical current
when there is no Josephson vortex in the weak link but there is a Pearl vortex
nearby.
