Ideal incompressible axisymmetric MHD: Uncovering finite-time singularities

Venkata Sai Swetha Kolluru; Rahul Pandit

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arXiv · 2507.06842

Ideal incompressible axisymmetric MHD: Uncovering finite-time singularities

Venkata Sai Swetha Kolluru·Rahul Pandit

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Abstract

We provide compelling numerical evidence for the development of (potential) finite-time singularities in the three-dimensional (3D) 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 C of the velocity and magnetic fields at the time of initialisation: (i) if C < 1, then the swirl components, at the wall, evolve towards 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 C = 1, there is no temporal evolution; (iii) if C > 1, then the swirl components, at the wall, evolve towards 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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Venkata Sai Swetha Kolluru, Rahul Pandit. 2025-07-09. Ideal incompressible axisymmetric MHD: Uncovering finite-time singularities. https://arxiv.org/abs/2507.06842

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