Appears in collection : 2026 - T2 - WS2 - Instabilities and transitions in geophysical flows

Magnetic fields do not change topology during smooth dynamics of ideal MHD. But topology change does occur in nature. Magnetic resistivity and near singularities have been suggested as a possible explanation.

In this talk I will focus on a different explanation, also suggested in the physics literature: reconnection due to magneto-hydrodynamic inertia. I will describe 2D models that exhibit rigorous ideal topology change. The models have global smooth solutions and the reconnection is obtained from merger of a pair of active scalars transported by incompressible velocities they create. Finite time merger without singularities and without resistivity or viscosity is proved rigorously.

Co-author: Zhongtian Hu