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arXiv · 1909.08678

Bounded solutions of ideal MHD with compact support in space-time

Daniel Faraco·Sauli Lindberg·László Székelyhidi Jr
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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.

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Daniel Faraco, Sauli Lindberg, László Székelyhidi Jr. 2019-09-18. Bounded solutions of ideal MHD with compact support in space-time. https://doi.org/10.1007/s00205-020-01570-y

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