We provide compelling numerical evidence for the development of (potential) finite-time singularities in the three-dimensional axisymmetric, ideal, incompressible magnetohydrodynamic (IMHD) equations, in a wall-bounded cylindrical domain, starting from smooth initial data, for the velocity and magnetic fields. We demonstrate that the nature of the singularity depends crucially on the relative strength $\mathcal{C}$ of the velocity and magnetic fields at the time of initialization: (i) if $\mathcal{C}<1$, then the swirl components, at the wall, evolve toward square profiles that lead to the intensification of shear at the meridional plane $(r=1,z=L/2)$ and the development of a finite-time singularity; (ii) if $\mathcal{C}=1$, there is no temporal evolution; (iii) if $\mathcal{C}>1$, then the swirl components, at the wall, evolve toward a cusp-type singularity. By examining the spatiotemporal evolution of the pressure, we obtain insights into the development of these singularities.

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• Magnetic fluids
• Direct numerical simulations