Abstract
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 language | English |
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Pages (from-to) | 51-93 |
Number of pages | 43 |
Journal | Archive for Rational Mechanics and Analysis |
Volume | 239 |
Issue number | 1 |
Early online date | 1 Jan 2020 |
DOIs | |
Publication status | Published - Jan 2021 |
MoE publication type | A1 Journal article-refereed |