Math @ Duke
|
Publications [#304582] of Jian-Guo Liu
Papers Published
- Liu, JG; Xin, Z, Convergence of the point vortex method for 2-D vortex sheet,
Mathematics of Computation, vol. 70 no. 234
(April, 2001),
pp. 595-606, American Mathematical Society (AMS) [doi]
(last updated on 2024/04/19)
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.
|
|
dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
| |
Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320
|
|