Magnetic helicity, weak solutions and relaxation of ideal MHD
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Published:2023-10-08
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Volume:
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ISSN:0010-3640
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Container-title:Communications on Pure and Applied Mathematics
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language:en
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Short-container-title:Comm Pure Appl Math
Author:
Faraco Daniel1,
Lindberg Sauli2,
Székelyhidi László3
Affiliation:
1. Universidad Autónoma de Madrid; ICMAT CSIC‐UAM‐UC3M‐UCM Madrid Spain
2. University of Helsinki Helsinki Finland
3. Universität Leipzig Leipzig Germany
Abstract
AbstractWe 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.
Funder
Ministerio de Ciencia e Innovación
European Research Council
Agencia Estatal de Investigación
Subject
Applied Mathematics,General Mathematics
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