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

Daniel Faraco, Sauli Lindberg, László Székelyhidi Jr

Published 2019-09-18Version 1

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.