Convergence of the point vortex method for 2-D vortex sheet

Liu, Jian-Guo; Xin, Zhouping

doi:10.1090/S0025-5718-00-01271-0

Convergence of the point vortex method for 2-D vortex sheet
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by Jian-Guo Liu and Zhouping Xin PDF

Math. Comp. 70 (2001), 595-606 Request permission

Abstract:

We give an elementary proof of the convergence of the point vortex method (PVM) to a classical weak solution for the two-dimensional incompressible Euler equations with initial vorticity being a finite 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 fields generated by the point vortex method do not have bounded local kinetic energy, the limiting velocity field is shown to have a bounded local kinetic energy.

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