  We consider the 2D Euler equations on $\R^2$ in vorticity form, with
unbounded initial vorticity, perturbed by a suitable non-smooth Kraichnan
transport noise, with regularity index $\alpha\in (0,1)$.
  We show weak existence for every $\dot{H}^{-1}$ initial vorticity. Thanks to
the noise, the solutions that we construct are limits in law of a regularized
stochastic Euler equation and enjoy an additional $L^2([0,T];H^{-\alpha})$
regularity.
  For every $p>3/2$ and for certain regularity indices $\alpha \in (0,1/2)$ of
the Kraichnan noise, we show also pathwise uniqueness for every $L^p$ initial
vorticity. This result is not known without noise.
