APDE seminar@UPV/EHU: On the topology of the magnetic lines of large solutions to the Magnetohydrodynamic equations in R3

Abstract

The purpose of this talk is to present the article [1], in which we establish two results: first, we introduce a new class of global strong solutions to the magnetohydrodynamic system in R3 with initial data (u_0, b_0) of arbitrarily large size in any critical space. To do so, we impose a smallness condition on the difference u_0 − b_0. Then we use this result to prove magnetic reconnection for a suitable class of (large) solutions. With this, we mean a change of topology of the integral lines of the magnetic field b under the evolution. The proof relies on counting the number of hyperbolic critical points of the solutions, and this instance is structurally stable. 

References

[1] Luc`a, R. and Pe ̃na, C. (2025) On the topology of the magnetic lines of large solutions to the Magnetohydrodynamic equations in R3. Preprint: arXiv:2505.09340.