Kinetic theory of point vortex systems from the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy

Abstract

Kinetic equations are derived from the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy for point vortex systems in an infinite plane. As the level of approximation for the Landau equation, the collision term of the kinetic equation derived coincides with that by Chavanis ({\it Phys. Rev. E} {\bf 64}, 026309 (2001)). Furthermore, we derive a kinetic equation corresponding to the Balescu-Lenard equation for plasmas, using the theory of the Fredholm integral equation. For large $N$, this kinetic equation is reduced to the Landau equation above.

10 pages, No figures. To be published in Physical Review E, 76-3

References in corpus (2)

• Algebraic Correlation Function and Anomalous Diffusion in the HMF model
• Slow relaxation in the two dimensional electron plasma under the strong magnetic field

Cited by in corpus (1)

• Two-dimensional Brownian vortices