Magnetic helicity, weak solutions and relaxation of ideal MHD

We revisit the issue of conservation of magnetic helicity and the Woltjer‐Taylor relaxation theory in magnetohydrodynamics (MHD) in the context of weak solutions. We introduce a relaxed system for the ideal MHD system, which decouples the effects of hydrodynamic turbulence such as the appearance of...

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Bibliographic Details
Published in:Communications on pure and applied mathematics 2024-04, Vol.77 (4), p.2387-2412
Main Authors: Faraco, Daniel, Lindberg, Sauli, Székelyhidi, László
Format: Article
Language:English
Subjects:
Conservation
Energy dissipation
Helicity
Magnetohydrodynamic turbulence
Plasma turbulence
Reynolds stress
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Summary:We revisit the issue of conservation of magnetic helicity and the Woltjer‐Taylor relaxation theory in magnetohydrodynamics (MHD) in the context of weak solutions. We introduce a relaxed system for the ideal MHD system, which decouples the effects of hydrodynamic turbulence such as the appearance of a Reynolds stress term from the magnetic helicity conservation in a manner consistent with observations in plasma turbulence. As by‐products we answer two open questions in the field: We show the sharpness of the L3 integrability condition for magnetic helicity conservation and provide turbulent bounded solutions for ideal MHD dissipating energy and cross helicity but with (arbitrary) constant magnetic helicity.
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.22168