  In this paper, we prove the first existence result of weak solutions to the
3D Euler equation with initial vorticity concentrated in a circle and velocity
field in $C([0,T],L^{2^-})$. The energy becomes finite and decreasing for
positive times, with vorticity concentrated in a ring that thickens and moves
in the direction of the symmetry axis. With our approach, there is no need to
mollify the initial data or to rescale the time variable. We overcome the
singularity of the initial data by applying convex integration within the
appropriate time-weighted space.
