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

被引：0

作者：

Kim, Chanwoo ^{[1
]}

Nguyen, Trinh T. ^{[1
]}

机构：

[1] Univ Wisconsin Madison, Dept Math, Madison, WI 53706 USA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2025年 / 406卷 / 04期

基金：

美国国家科学基金会;

关键词：

NAVIER-STOKES EQUATIONS; INCOMPRESSIBLE FLUID-MECHANICS; BOLTZMANN-EQUATION; INVISCID LIMIT; KINETIC-EQUATIONS; DYNAMICAL LIMIT; VORTEX MERGER; DIMENSIONS; CONVERGENCE; BOUNDARY;

D O I：

10.1007/s00220-025-05264-y

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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.

引用

页数：49

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