The vortex-wave system is the coupling of the 2D vorticity equation with the point-vortex system, and it is a model for the motion of sharply concentrated vórtices within a smooth(er) vorticity background. This system was introduced by Marchioro and Pulvirenti in 1991. In this talk we will give a fairly complete look at what is known and what is not known about this system.
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