On Moffatt’s Magnetic Relaxation Equations

Rajendra Beekie; Susan Friedlander; Vlad Vicol

doi:10.1007/s00220-021-04289-3

On Moffatt’s Magnetic Relaxation Equations

Rajendra Beekie, Susan Friedlander, Vlad Vicol

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the stability properties for a family of equations introduced by Moffatt to model magnetic relaxation. These models preserve the topology of magnetic streamlines, contain a cubic nonlinearity, and yet have a favorable L² energy structure. We consider the local and global in time well-posedness of these models and establish a difference between the behavior as t→ ∞ with respect to weak and strong norms.

Original language	English (US)
Pages (from-to)	1311-1339
Number of pages	29
Journal	Communications In Mathematical Physics
Volume	390
Issue number	3
DOIs	https://doi.org/10.1007/s00220-021-04289-3
State	Published - Mar 2022

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-021-04289-3

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title = "On Moffatt{\textquoteright}s Magnetic Relaxation Equations",

abstract = "We investigate the stability properties for a family of equations introduced by Moffatt to model magnetic relaxation. These models preserve the topology of magnetic streamlines, contain a cubic nonlinearity, and yet have a favorable L2 energy structure. We consider the local and global in time well-posedness of these models and establish a difference between the behavior as t→ ∞ with respect to weak and strong norms.",

author = "Rajendra Beekie and Susan Friedlander and Vlad Vicol",

note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

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AB - We investigate the stability properties for a family of equations introduced by Moffatt to model magnetic relaxation. These models preserve the topology of magnetic streamlines, contain a cubic nonlinearity, and yet have a favorable L2 energy structure. We consider the local and global in time well-posedness of these models and establish a difference between the behavior as t→ ∞ with respect to weak and strong norms.

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On Moffatt’s Magnetic Relaxation Equations

Abstract

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