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Auteurs principaux: Liao, Shasha, Lin, Zhiwu, Zhu, Hao
Format: Preprint
Publié: 2023
Sujets:
Accès en ligne:https://arxiv.org/abs/2304.00264
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author Liao, Shasha
Lin, Zhiwu
Zhu, Hao
author_facet Liao, Shasha
Lin, Zhiwu
Zhu, Hao
contents Kelvin-Stuart vortices are classical mixing layer flows with many applications in fluid mechanics, plasma physics and astrophysics. We prove that the whole family of Kelvin-Stuart vortices is nonlinearly orbitally stable for co-periodic perturbations, and linearly unstable for multi-periodic and modulational perturbations. This verifies a long-standing conjecture since the discovery of the Kelvin-Stuart cat's-eye flows in the 1960s. Kelvin-Stuart cat's eyes also appear as magnetic islands which are magnetostatic equilibria for the planar ideal MHD equations in plasmas. We prove nonlinear orbital stability of Kelvin-Stuart magnetic islands for co-periodic perturbations, and give the first rigorous proof of coalescence instability for the whole family, which is important for magnetic reconnection.
format Preprint
id arxiv_https___arxiv_org_abs_2304_00264
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle On the stability and instability of Kelvin-Stuart cat's-eye flows
Liao, Shasha
Lin, Zhiwu
Zhu, Hao
Analysis of PDEs
Kelvin-Stuart vortices are classical mixing layer flows with many applications in fluid mechanics, plasma physics and astrophysics. We prove that the whole family of Kelvin-Stuart vortices is nonlinearly orbitally stable for co-periodic perturbations, and linearly unstable for multi-periodic and modulational perturbations. This verifies a long-standing conjecture since the discovery of the Kelvin-Stuart cat's-eye flows in the 1960s. Kelvin-Stuart cat's eyes also appear as magnetic islands which are magnetostatic equilibria for the planar ideal MHD equations in plasmas. We prove nonlinear orbital stability of Kelvin-Stuart magnetic islands for co-periodic perturbations, and give the first rigorous proof of coalescence instability for the whole family, which is important for magnetic reconnection.
title On the stability and instability of Kelvin-Stuart cat's-eye flows
topic Analysis of PDEs
url https://arxiv.org/abs/2304.00264