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A rigorous derivation of point vortex systems from kinetic equations has beena challenging open problem, due to singular layers in the inviscid limit,giving a large velocity gradient in the Boltzmann equations. In this paper, wederive the Helmholtz-Kirchhoff point-vortex system from the hydrodynamic limitsof the Boltzmann equations. We construct Boltzmann solutions by theHilbert-type expansion associated to the point vortices solutions of the 2DNavier-Stokes equations. We give a precise pointwise estimate for the solutionof the Boltzmann equations with small Strouhal number and Knudsen number.

Asymptotics of Helmholtz-Kirchhoff Point-Vortices in the Phase Space