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<p>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.</p>

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On the stability and instability of Kelvin–Stuart cat’s-eye flows

  • 期刊论文

  • 发表日期：

    2026年5月14日

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  • Shasha Liao,
  • Zhiwu Lin,
  • Hao Zhu

摘要

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.