Bounded solutions of ideal MHD with compact support in space-time
arXiv:1909.08678 · doi:10.1007/s00205-020-01570-y
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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- On the conservation of helicity by weak solutions of the 3D Euler and inviscid MHD equations
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- Large amplitude traveling waves for the non-resistive MHD system
- On the energy-constrained optimal mixing problem for one-dimensional initial configurations
- An extension theorem for weak solutions of the 3d incompressible Euler equations and applications to singular flows
- The Rayleigh-Taylor instability with local energy dissipation