3 citations · 6 across the 9 of their papers we have counts for
9 papers
Variational Principles for Shock Dynamics in Compressible Euler Flows
François Gay-Balmaz, Cheng Yang
Hamilton's principle plays a central role in fluid mechanics as a fundamental tool for deriving governing equations, analyzing conservation laws, and designing structure-preserving…
The helicity uniqueness conjecture in 3D hydrodynamics
Boris Khesin, Daniel Peralta-Salas, Cheng Yang
We prove that the helicity is the only regular Casimir function for the coadjoint action of the volume-preserving diffeomorphism group on smooth exact divergence-…
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…
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…
Averaging, symplectic reduction, and central extensions
Cheng Yang, Boris Khesin
We show that the averaged equation for a one-frequency fast-oscillating Hamiltonian system is the result of symplectic reduction of a certain natural system on the corresponding $S…
On the Hamiltonian and Geometric structure of the Craik-Leibovich equation
Cheng Yang
In this paper we show that the Craik-Leibovich (CL) equation in hydrodynamics is the Euler equation on the dual of a certain central extension of the Lie algebra of divergence-free…