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arXiv · 2303.12257

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

Chanwoo Kim·Trinh T. Nguyen
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Abstract

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.

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Chanwoo Kim, Trinh T. Nguyen. 2023-03-22. Asymptotics of Helmholtz-Kirchhoff Point-Vortices in the Phase Space. https://arxiv.org/abs/2303.12257

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