Formation of Finite Time Singularity for Axially Symmetric Magnetohydrodynamic Waves in 3-D

In this paper we study the compressible magnetohydrodynamics equations in three dimensions, which offer a good model for plasmas. Formation of singularity for \(C^1\) $C^1$ -solution in finite time is proved with axisymmetric initial data. The key observation is that the magnetic force term admits a good structure with axisymmetric assumption.