This research reveals nonuniqueness in ideal MHD formulations, indicating implications for weak solutions.
In this paper, we establish the non-uniqueness of solutions to the ideal magnetohydrodynamics equations in any dimension greater than three by proving the existence of infinitely many compactly supported weak solutions. In particular, these solutions fail to conserve the total energy. Our proof relies on the differential inclusion framework tailored to the geometry of ideal MHD system, which enables the simultaneous use of Baire category method and convex integration scheme.
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Miao et al. (2025) studied this question.