相空间中Helmholtz-Kirchhoff点涡的渐近性

IF 2.2 1区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Communications in Mathematical Physics Pub Date : 2025-04-02 DOI:10.1007/s00220-025-05264-y

Chanwoo Kim, Trinh T. Nguyen

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引用次数: 0

摘要

从动力学方程中严格推导点涡系统一直是一个具有挑战性的开放问题，因为在无粘极限中存在奇异层，在玻尔兹曼方程中会产生很大的速度梯度。本文从玻尔兹曼方程的水动力极限出发，导出了Helmholtz-Kirchhoff点涡系统。我们通过与二维Navier-Stokes方程的点涡解相关的hilbert型展开构造Boltzmann解。给出了具有小Strouhal数和Knudsen数的玻尔兹曼方程解的精确的逐点估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

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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来源期刊

Communications in Mathematical Physics 物理-物理：数学物理

CiteScore

4.70

自引率

8.30%

发文量

226

审稿时长

3-6 weeks

期刊介绍： The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.