Cluster of vortex helices in the incompressible $3$d Euler equations
Ignacio Guerra, Monica Musso
TL;DR
This paper proves the existence of multiple vortex helices in a 3D incompressible Euler fluid that collapse into each other, revealing complex vortex interactions in ideal fluids.
Contribution
It introduces the first rigorous proof of vortex helices collapsing in 3D Euler equations, advancing understanding of vortex dynamics.
Findings
Existence of collapsing vortex helices proven
Multiple helical filaments can converge in 3D Euler flows
Provides mathematical foundation for vortex filament interactions
Abstract
In an inviscid and incompressible fluid in dimension 3, we prove the existence of several helical filaments, or vortex helices, collapsing into each others.
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Taxonomy
TopicsNavier-Stokes equation solutions · Aquatic and Environmental Studies