Math @ Duke

Publications [#304582] of JianGuo Liu
Papers Published
 Liu, JG; Xin, Z, Convergence of the point vortex method for 2D vortex sheet,
Mathematics of Computation, vol. 70 no. 234
(2001),
pp. 595606 [doi]
(last updated on 2018/11/20)
Abstract: We give an elementary proof of the convergence of the point vortex method (PVM) to a classical weak solution for the twodimensional 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 KelvinHelmholtz 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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