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.

中文翻译：

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时空紧支的理想MHD有界解

我们表明，在 3 维理想磁流体动力学中，存在无限多的有界解，这些解在时空中得到紧密支持，并且具有非平凡的速度和磁场。该解决方案违反了总能量守恒和交叉螺旋性，但保留了磁螺旋性。对于二维情况，我们表明，相比之下，能量空间中不存在非平凡的紧支持解。