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

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