arXiv:2303.12257 Abstract | arXiv Analytics

arXiv:2303.12257 [math.AP]Abstract References Reviews Resources

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

Published 2023-03-22Version 1

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

Comments: 52 pages

Categories: math.AP, math-ph, math.MP

Keywords: phase space, boltzmann equations, asymptotics, point vortices solutions, small strouhal number

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