The vortex-wave system is the coupling of the 2D vorticity equation, for the evolution of a continuous distribution of vorticity, with the point-vortex system. This terminology was introduced by Marchioro and Pulvirenti in 1991. They also proved existence and uniqueness of solutions when the initial data is a vortex patch with point vortices outside the patch, a result recently generalized by Lacave and Miot.

In this talk we will explore the known theory for the vortex-wave system. Our main result is existence of a suitably defined weak solution for vorticity in Lp, p > 2.