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


Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Liu, JG; Xin, Z

Published Date

  • April 1, 2001

Published In

Volume / Issue

  • 70 / 234

Start / End Page

  • 595 - 606

International Standard Serial Number (ISSN)

  • 0025-5718

Digital Object Identifier (DOI)

  • 10.1090/S0025-5718-00-01271-0

Citation Source

  • Scopus