Proof of Taylor's Conjecture on Magnetic Helicity Conservation
Abstract
We prove the mathematical version of 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.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 May 2019
 DOI:
 10.1007/s00220019034227
 arXiv:
 arXiv:1806.09526
 Bibcode:
 2019CMaPh.373..707F
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 35Q35;
 76W05;
 76B03
 EPrint:
 30 pages, 2 figures