Convergence of a point vortex method for vortex sheets

Based on the observation that a point vortex approximation can be made spectrally accurate by using Van de Vooren’s desingularization, short time convergence of the point vortex method for both vortex sheets and the Boussinesq approximation are proved using analytic data. The spectral accuracy of the method allows a very simple proof to be obtained without using the Cauchy–Kowalewski theorem.