Global large solutions exist for incompressible MHD equations with small Alfvén numbers when viscosity and resistivity are both positive.
Majda, Compressible fluid flow and systems of conservation laws in several space variables, volume 53 ofApplied Mathematical Sciences, Springer-Verlag, New York
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On Global-in-time Solutions of Incompressible MHD Equations with Small Alfv\'en Numbers
Global large solutions exist for incompressible MHD equations with small Alfvén numbers when viscosity and resistivity are both positive.