Twisting in Hamiltonian flows and perfect fluids

• 成果类型: Article
• 署名作者: Drivas, Theodore D.; Elgindi, Tarek M.; Jeong, In-Jee
• 署名单位: State University of New York (SUNY) System; Stony Brook University; Duke University; Seoul National University (SNU); Seoul National University (SNU)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01285-x
• 发表日期: 2024
• 页码: 331-370
• 关键词: inherent instability; nonlinear stability; vorticity-gradient; Euler equation; vortex; GROWTH; smoothness; REGULARITY

摘要

We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to establish a number of results that reveal a form of irreversibility in the Euler equations governing the motion of an incompressible and inviscid fluid. In particular, we show that nearby general stable steady states (i) all fluid flows exhibit indefinite twisting (ii) vorticity generically exhibits gradient growth and wandering. We also give examples of infinite time gradient growth for smooth solutions to the SQG equation and of smooth vortex patches that entangle and develop unbounded perimeter in infinite time.