【青年学者论坛】Stability and instability of Kelvin-Stuart cat's eyes flows
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题目：Stability and instability of Kelvin-Stuart cat's eyes flows
报告人：朱昊 Hao Zhu，Nanjing University
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 stable for co-periodic perturbations, and linearly unstable for multi-periodic or modulational perturbations. This verifies a conjecture since the discovery of the Kelvin-Stuart cat's eyes flows in the 1960s. Kelvin-Stuart cat's eyes also appear as magnetic islands which are magnetostatic equilibria for the 2D ideal MHD equations in plasmas. We prove nonlinear stability of Kelvin-Stuart magnetic islands for co-periodic perturbations, and give a rigorous proof of the coalescence instability, which is important for magnetic reconnection. This talk is based on a joint work with Shasha Liao and Zhiwu Lin.