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

Authors:
Jian-Guo Liu and Zhouping Xin

Journal:
Math. Comp. **70** (2001), 595-606

MSC (2000):
Primary 65M06, 76M20

DOI:
https://doi.org/10.1090/S0025-5718-00-01271-0

Published electronically:
April 13, 2000

MathSciNet review:
1813141

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Jian-Guo Liu**

Affiliation:
Institute for Physical Science and Technology and Department of Mathematics, University of Maryland, College Park, MD 20742

Email:
jliu@math.umd.edu

**Zhouping Xin**

Affiliation:
Courant Institute, New York University and IMS and Dept. of Math., The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

Email:
xinz@cims.nyu.edu

DOI:
https://doi.org/10.1090/S0025-5718-00-01271-0

Keywords:
Point vortex method,
vortex sheet,
incompressible Euler equations,
classical weak solution

Received by editor(s):
May 24, 1999

Published electronically:
April 13, 2000

Article copyright:
© Copyright 2000
American Mathematical Society