  In this paper we construct unstable shocks in the context of 2D isentropic
compressible Euler in azimuthal symmetry. More specifically, we construct
initial data that when viewed in self-similar coordinates, converges
asymptotically to the unstable $C^{\frac15}$ self-similar solution to the
Burgers' equation. Moreover, we show the behavior is stable in $C^8$ modulo a
two dimensional linear subspace. Under the azimuthal symmetry assumption, one
cannot impose additional symmetry assumptions in order to isolate the
corresponding manifold of initial data leading to stability: rather, we rely on
modulation variable techniques in conjunction with a Newton scheme.
