Asymptotics of Helmholtz-Kirchhoff Point-Vortices in the Phase Space
| Autor: | Kim, Chanwoo, Nguyen, Trinh T. |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 52 pages |
| Databáze: | arXiv |
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