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arXiv · 2603.21800

Non-uniqueness of smooth solutions of the 5D magnetohydrodynamic equations from critical data

Zipeng Chen·Song Liu·Zhaoyang Yin
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Abstract

Recently, Coiculescu and Palasek \cite{Coiculescu2025} shows the non-uniqueness of solutions for the 3D incompressible Navier-Stokes equations with initial data in $BMO^{-1}$. Inspired by their breakthrough work, we develop their schemes for the incompressible magnetohydrodynamic equations and obtain a similar result in 5 dimensional case. More precisely, we construct two distinct global solutions with a initial data, which has nonvanishing velocity and magnetic fields in $BMO^{-1}(\mathbb{T}^5)$.

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Zipeng Chen, Song Liu, Zhaoyang Yin. 2026-03-23. Non-uniqueness of smooth solutions of the 5D magnetohydrodynamic equations from critical data. https://arxiv.org/abs/2603.21800

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