2018/06/25 by Daniel Faraco, Sauli Lindberg · 1 citation
Mathematics · Physics and Astronomy · #Conjecture #Conserved quantity #Domain (mathematical analysis) #Geometric Analysis and Curvature Flows #Helicity #Ideal (ethics) #Limit (mathematics) #Magnetic field #Magnetic helicity #Navier-Stokes equation solutions #Numerical methods in inverse problems #math-ph #math.AP #math.MP #msc:35Q35 #msc:76B03 #msc:76W05
paper · pdf · doi:10.1007/s00220-019-03422-7
30 pages, 2 figures
arxiv created 2018/06/25 · openalex created_date 2018/07/10 · openalex publication_date 2019/05/06 · arxiv updated 2019/05/22 · openalex updated_date 2026/08/05
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.