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

Publication
, Journal Article

Liu, JG; Xin, Z

Published in: Mathematics of Computation

April 1, 2001

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.

### Duke Scholars

## Published In

Mathematics of Computation

## DOI

## ISSN

0025-5718

## Publication Date

April 1, 2001

## Volume

70

## Issue

234

## Start / End Page

595 / 606

## Related Subject Headings

- Numerical & Computational Mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics

### Citation

APA

Chicago

ICMJE

MLA

NLM

Liu, J. G., & Xin, Z. (2001). Convergence of the point vortex method for 2-D vortex sheet.

*Mathematics of Computation*,*70*(234), 595–606. https://doi.org/10.1090/S0025-5718-00-01271-0Liu, J. G., and Z. Xin. “Convergence of the point vortex method for 2-D vortex sheet.”

*Mathematics of Computation*70, no. 234 (April 1, 2001): 595–606. https://doi.org/10.1090/S0025-5718-00-01271-0.Liu JG, Xin Z. Convergence of the point vortex method for 2-D vortex sheet. Mathematics of Computation. 2001 Apr 1;70(234):595–606.

Liu, J. G., and Z. Xin. “Convergence of the point vortex method for 2-D vortex sheet.”

*Mathematics of Computation*, vol. 70, no. 234, Apr. 2001, pp. 595–606.*Scopus*, doi:10.1090/S0025-5718-00-01271-0.Liu JG, Xin Z. Convergence of the point vortex method for 2-D vortex sheet. Mathematics of Computation. 2001 Apr 1;70(234):595–606.

## Published In

Mathematics of Computation

## DOI

## ISSN

0025-5718

## Publication Date

April 1, 2001

## Volume

70

## Issue

234

## Start / End Page

595 / 606

## Related Subject Headings

- Numerical & Computational Mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics