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Consideration in this paper is the global well-posedness for the 3Daxisymmetric MHD equations with only vertical dissipation and vertical magneticdiffusion. The existence of unique low-regularity global solutions of thesystem with initial data in Lorentz spaces is established by using higher-orderenergy estimates and real interpolation method.

Low regularity global well-posedness of axisymmetric MHD equations with vertical dissipation and magnetic diffusion