1. On the stability and instability of Kelvin-Stuart cat's eyes flows
- Author
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Liao, Shasha, Lin, Zhiwu, and Zhu, Hao
- Subjects
Mathematics - Analysis of PDEs - Abstract
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 long-standing 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 the first rigorous proof of the coalescence instability, which is important for magnetic reconnection., Comment: 124 pages. We added a comment on the stability/instability of Taylor's 2-parameter family of cat's eyes solutions, and added Lemma 3.7
- Published
- 2023