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arXiv · 2606.21040

Non-uniqueness for the hypo-dissipative compressible 3D magnetohydrodynamic equations

Haobin Li·Peng Qu
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Abstract

We consider the compressible 3D magnetohydrodynamic (MHD) equations under general pressure laws. For all hypo-viscosities $(-\Delta)^{\alpha_1}$ and hypo-resistivity $(-\Delta)^{\alpha_2}$ with $\alpha_1,\alpha_2\in(0,1)$, we prove the non-uniqueness of weak solutions to 3D MHD equations which reveals that there exist infinitely many weak solutions with the same initial data. Also, for the weak solutions in $C^{\widetilde{\beta}}_{t,x}$ to the compressible ideal MHD, where $\widetilde{\beta}>0$, we prove that they are the strong vanishing viscosity and resistivity limit of the weak solutions to the hypo-dissipative compressible MHD.

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Haobin Li, Peng Qu. 2026-06-19. Non-uniqueness for the hypo-dissipative compressible 3D magnetohydrodynamic equations. https://arxiv.org/abs/2606.21040

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