Global existence for 3D anisotropic MHD system with horizontal dissipation and small horizontal variations

This is the authors' abstract. We don't add key points for this paper.

This paper establishes the global well-posedness for the 3D anisotropic MHD system with partial dissipation: Δ h ⁢ 𝑢 for velocity and ∂ 2 1 𝑏 for magnetic field, near the background field ( 0 , 1 , 0 ) . Crucially, only horizontal components ( 𝑢 h 0 , 𝑏 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.