3 problems

Let $u$ be a smooth solution of the incompressible Euler equations in $4\mathbb{R}^3$ whose vorticity is initially concentrated near a smooth curve. Let the curve evolve according…

An isolated vortex filament in a three-dimensional inviscid fluid is a curve representing concentrated vorticity, and the binormal flow is the evolution law in which the filament m…

Let a regular planar polygon evolve according to the binormal flow. At rational multiples of the time period, consider the resulting curve and the angle between consecutive sides.…