| Abstract: |
| In this talk, we first revisit the vortex filament conjecture for three-dimensional incompressible Euler flows with helical symmetry and no swirl. By adapting gluing methods, we obtain the first construction of a smooth helical vortex filament in the whole space $\mathbb{R}^3$ whose cross-sectional vorticity remains compactly supported in $\mathbb{R}^2$ for all times. Building on this construction, we then investigate the leapfrogging phenomenon of helical vortex filaments, in which several interacting vortex helices with a common symmetry axis alternately overtake one another while preserving their coherent structure. This is joint work with Monica Musso. |
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