  This article studies the vortex-wave system for the Surface Quasi-Geostrophic
equation with parameter 0 < s < 1. We obtained local existence of classical
solutions in H^4 under the standard "plateau hypothesis", H^2-stability of the
solutions, and a blow-up criterion. In the sub-critical case s > 1/2 we
established global existence of weak solutions. For the critical case s = 1/2,
we introduced a weaker notion of solution (V-weak solutions) to give a meaning
to the equation and prove global existence.
