Global large solutions exist for incompressible MHD equations with small Alfvén numbers when viscosity and resistivity are both positive.
Zhang, Singular limit of the nonisentropic compressible ideal MHD equations in a domain with boundary, Appl
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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.