In the recent paper [ 11 ], the authors provided the first construction of classical solutions for Euler equations featuring leapfrogging motion for any time, by desingularizing via concentrated vortex patches a suitable four-point vortex dynamics in the plane. In this note, we show that the leapfrogging motion persists for very long times by replacing such patches with quite general initial data of concentrated vorticity.
Remarks on the Leapfrogging Motion for Planar Euler Equations / Butta', Paolo; Cavallaro, Guido; Marchioro, Carlo. - In: REPORTS ON MATHEMATICAL PHYSICS. - ISSN 0034-4877. - 96:3(2025), pp. 343-355. [10.1016/s0034-4877(25)00078-3]
Remarks on the Leapfrogging Motion for Planar Euler Equations
Butta', Paolo;Cavallaro, Guido;Marchioro, Carlo
2025
Abstract
In the recent paper [ 11 ], the authors provided the first construction of classical solutions for Euler equations featuring leapfrogging motion for any time, by desingularizing via concentrated vortex patches a suitable four-point vortex dynamics in the plane. In this note, we show that the leapfrogging motion persists for very long times by replacing such patches with quite general initial data of concentrated vorticity.| File | Dimensione | Formato | |
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