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Ideal incompressible axisymmetric MHD: Uncovering finite-time singularities

Sai Swetha Venkata Kolluru* and Rahul Pandit†

  • *Contact author: venkata-saiswetha.kolluru@cea.fr
  • †Contact author: rahul@iisc.ac.in
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Phys. Rev. Fluids 11, 063701 – Published 10 June, 2026

DOI: https://doi.org/10.1103/l645-3ljm

Abstract

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 C of the velocity and magnetic fields at the time of initialization: (i) if 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 C=1, there is no temporal evolution; (iii) if 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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Information

Phys. Rev. Fluids 11, 063701– Published 10 June, 2026
  • Received 28 September 2025
  • Accepted 14 May 2026
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