Convergence of the Point Vortex Methodfor 2 - D Vortex

We give an elementary proof of the convergence of the point vor-tex method (PVM) to a classical weak solution for the two-dimensional incom-pressible Euler equations with initial vorticity being a nite Radon measure of distinguished sign and the initial velocity of locally bounded energy. This includes the important example of vortex sheets, which exhibits the classical Kelvin-Helmholtz instability. A surprise fact is that although the velocity elds generated by the point vortex method do not have bounded local kinetic energy, the limiting velocity eld is shown to have a bounded local kinetic energy.