Convergence of point vortex method for 2-D vortex sheet

Jian-Guo Liu University of Maryland Zhouping Xin New York University and IMS and Dept

Analysis of PDEs mathscidoc:1702.03068

595 - 606 , 70, (234), 595-606 , 2001.1
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.
. Point vortex method, vortex sheet, incompressible Euler equations, classical weak solution.
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@inproceedings{jian-guo2001convergence,
  title={Convergence of point vortex method for 2-D vortex sheet},
  author={Jian-Guo Liu, and Zhouping Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209112620883061386},
  booktitle={595 - 606 },
  volume={70},
  number={234},
  pages={595-606 },
  year={2001},
}
Jian-Guo Liu, and Zhouping Xin. Convergence of point vortex method for 2-D vortex sheet. 2001. Vol. 70. In 595 - 606 . pp.595-606 . http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209112620883061386.
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