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arXiv · 2606.05764

Global Existence for 3D Anisotropic MHD system with Horizontal Dissipation and Small Horizontal Variations

Qiliang Lin·Chenyin Qian·Daoyao Zhou
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Abstract

This paper establishes the global well-posedness for the 3D anisotropic MHD system with partial dissipation: $\Delta_\mathrm{h}u$ for velocity and $\partial_1^2b$ for magnetic field, near background field $(0,1,0)$. Crucially, only horizontal components $(u^\mathrm{h}_0,b^\mathrm{h}_0)$ need to be small in $H^2(\R^3)$, while $(u^3_0,b^3_0)$ can be arbitrarily large. Our analysis develops novel techniques including component-decoupled energies and iterative control of dangerous nonlinearities using the background field structure. This establishes the global result for anisotropic MHD equations allowing large vertical data, breaking the full-smallness requirement of previous works.

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Qiliang Lin, Chenyin Qian, Daoyao Zhou. 2026-06-04. Global Existence for 3D Anisotropic MHD system with Horizontal Dissipation and Small Horizontal Variations. https://arxiv.org/abs/2606.05764

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