Non-uniqueness of weak solutions to the 3-D stationary MHD equations in Besov space with negative regularity index

Peng Qu; Mingxin Zhang

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arXiv · 2606.16141

Non-uniqueness of weak solutions to the 3-D stationary MHD equations in Besov space with negative regularity index

Peng Qu·Mingxin Zhang

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Abstract

In this paper, we study the 3-D incompressible fractional stationary MHD equations on the torus $\mathbb{T}^3$. For fractional power indices $\alpha_1,\alpha_2 >0,$ we prove that there exist infinite non-trivial stationary singular solutions of 3-D fractional MHD equations via convex integration. In particular, this result shows the non-uniqueness of weak solutions to the 3-D stationary MHD equations in some sub-critical Besov spaces.

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Peng Qu, Mingxin Zhang. 2026-06-15. Non-uniqueness of weak solutions to the 3-D stationary MHD equations in Besov space with negative regularity index. https://arxiv.org/abs/2606.16141

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