This article demonstrates magnetic reconnection in global strong solutions to magnetohydrodynamic equations, highlighting topology changes in integral lines.
The purpose of this article is twofold: first, we introduce a new class of global strong solutions to the magnetohydrodynamic system in R³ with initial data (u₀,b₀) of arbitrarily large size in any critical space. To do so, we impose a smallness condition on the difference u₀-b₀. 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.
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Lucà et al. (2025) studied this question.
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