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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:

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

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