Bounded Solutions of Ideal MHD with Compact Support in Space-Time

Daniel Faraco, Sauli Lindberg, László Székelyhidi*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
36 Downloads (Pure)


We show that in 3-dimensional ideal magnetohydrodynamics there exist infinitely many bounded solutions that are compactly supported in space-time and have non-trivial velocity and magnetic fields. The solutions violate conservation of total energy and cross helicity, but preserve magnetic helicity. For the 2-dimensional case we show that, in contrast, no nontrivial compactly supported solutions exist in the energy space.

Original languageEnglish
Pages (from-to)51-93
Number of pages43
JournalArchive for Rational Mechanics and Analysis
Issue number1
Early online date1 Jan 2020
Publication statusPublished - Jan 2021
MoE publication typeA1 Journal article-refereed

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