On the equations of 212D electron magnetohydrodynamics

The 212D model of electron magnetohydrodynamics is obtained when we allow the magnitudes to depend only on two spatial variables. While the a priori estimates need for an existence theorem are rather tricky in the full three-dimensional case, these estimates may be obtained in 212D EMHD with Sobolev spaces considerably larger than the ones needed for other nonlinear fluid equations such as Euler’s. The reason why such a priori bounds do not work for the maximum norm is also analysed: it turns out that the saddle points of the current are the barrier which could allow in principle an unbounded growth of the maximum of the main magnitudes for certain initial conditions.