Proof of Taylor's conjecture on magnetic helicity conservation

Abstract

We prove Taylor's conjecture which says that in 3D MHD, magnetic helicity is conserved in the ideal limit in bounded, simply connected, perfectly conducting domains. When the domain is multiply connected, magnetic helicity depends on the vector potential of the magnetic field. In that setting we show that magnetic helicity is conserved for a large and natural class of vector potentials but not in general for all vector potentials. As an analogue of Taylor's conjecture in 2D, we show that mean square magnetic potential is conserved in the ideal limit, even in multiply connected domains.

30 pages, 2 figures

References in corpus (2)

• Coarse-Grained Incompressible Magnetohydrodynamics: analyzing the turbulent cascades
• Nonuniversality and finite dissipation in decaying magnetohydrodynamic turbulence

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• On the conservation of helicity by weak solutions of the 3D Euler and inviscid MHD equations
• On the topology of the magnetic lines of solutions of the MHD equations
• A study of global magnetic helicity in self-consistent spherical dynamos