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math-ph2019★ 1 cited
Higher-dimensional Euler fluids and Hasimoto transform: counterexamples and generalizations
Boris Khesin, Cheng Yang
The binormal (or vortex filament) equation provides the localized induction approximation of the 3D incompressible Euler equation. We present explicit solutions of the binormal equ…
math-ph2019★ 1 cited
A basis of Casimirs in 3D magnetohydrodynamics
Boris Khesin, Daniel Peralta-Salas, Cheng Yang
We prove that any regular Casimir in 3D magnetohydrodynamics is a function of the magnetic helicity and cross-helicity. In other words, these two helicities are the only independen…