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Convergence of the point vortex method for 2-D vortex sheet
Author(s):
Jian-Guo
Liu;
Zhouping
Xin.
Journal:
Math. Comp.
70
(2001),
595-606.
MSC (2000):
Primary 65M06, 76M20
Posted:
April 13, 2000
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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:
10.1090/S0025-5718-00-01271-0
PII:
S 0025-5718(00)01271-0
Keywords:
Point vortex method,
vortex sheet,
incompressible Euler equations,
classical weak solution
Received by editor(s):
May 24, 1999
Posted:
April 13, 2000
Copyright of article:
Copyright
2000,
American Mathematical Society
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