Magnetic helicity, weak solutions and relaxation of ideal MHD
Analysis of PDEs
2021-09-21 v1 Plasma Physics
Abstract
We revisit the issue of conservation of magnetic helicity and the Woltjer-Taylor relaxation theory in magnetohydrodynamics 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 integrability condition for magnetic helicity conservation and provide turbulent bounded solutions for MHD dissipating energy and cross helicity but with (arbitrary) constant magnetic helicity.
Keywords
Cite
@article{arxiv.2109.09106,
title = {Magnetic helicity, weak solutions and relaxation of ideal MHD},
author = {Daniel Faraco and Sauli Lindberg and László Székelyhidi},
journal= {arXiv preprint arXiv:2109.09106},
year = {2021}
}
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23 pages