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Leapfrogging vortex rings for the three‐dimensional incompressible Euler equations
Communications on Pure and Applied Mathematics ( IF 3 ) Pub Date : 2024-05-06 , DOI: 10.1002/cpa.22199 Juan Dávila 1 , Manuel del Pino 1 , Monica Musso 1 , Juncheng Wei 2
Communications on Pure and Applied Mathematics ( IF 3 ) Pub Date : 2024-05-06 , DOI: 10.1002/cpa.22199 Juan Dávila 1 , Manuel del Pino 1 , Monica Musso 1 , Juncheng Wei 2
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A classical problem in fluid dynamics concerns the interaction of multiple vortex rings sharing a common axis of symmetry in an incompressible, inviscid three‐dimensional fluid. In 1858, Helmholtz observed that a pair of similar thin, coaxial vortex rings may pass through each other repeatedly due to the induced flow 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.
更新日期：2024-05-06
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