| Abstract: |
| Leapfrogging motion describes a phenomenon in which two or more vortex rings, or other entities such as point vortices, repeatedly pass through each other. This occurs because the induced flow generated by one vortex ring causes it to accelerate and move through the other, after which the roles reverse. The resulting motion is a time-periodic solution in certain fluid models. Although this behavior has long been observed in experiments and numerical simulations, a rigorous mathematical construction has remained elusive. In this talk, we will first review some known results on leapfrogging motion for point vortices and vortex rings, and then present new analytical approaches to describe such phenomena. |
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