Speaker: Juncheng Wei ，英属哥伦比亚大学、香港中文大学

Inviter: 范晨捷副研究员

Title: Leapfrogging vortex rings for three-dimensional Euler equations

Language: English

Time & Venue: 2025.06.27 14:00-15:00 南楼N202

Abstract: A classical problem in fluid dynamics concerns the interaction of multiple vortex rings sharing a common axis of symmetry in an incompressible, inviscid 3-dimensional fluid. Helmholtz (1858) observed that a pair of similar thin, coaxial vortex rings may pass through each other repeatedly due to the induced ow of the rings acting on each other. This celebrated configuration, known as leapfrogging, has not yet been rigorously established. We provide a mathematical justification for this phenomenon by constructing a smooth solution of the 3d Euler equations exhibiting this motion pattern. This is a special case of so-called Vortex-Filament Conjecture, which is still largely open. (Joint work with Juan Davila, Manuel del Pino and Monica Musso.)