The Magnetohydrodynamics (MHD) equations describe the evolution of an electrically conducting fluid under the interaction of velocity and magnetic fields. In the ideal (non-resistive) case, Alfvén’s theorem implies that the topology of magnetic field lines is preserved by the flow. In contrast, in the resistive case the magnetic field may undergo reconnection, meaning that the topology of its field lines can change in time. This phenomenon plays a central role in various astrophysical processes, but it is still far from being fully understood from an analytical and theoretical point of view.

In this talk, I will discuss recent constructions of smooth solutions to the resistive MHD equations exhibiting magnetic reconnection, providing mathematically rigorous examples of this phenomenon.