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

Abstract

Consideration in this paper is the global well-posedness for the 3D axisymmetric MHD equations with only vertical dissipation and vertical magnetic diffusion. The existence of unique low-regularity global solutions of the system with initial data in Lorentz spaces is established by using higher-order energy estimates and real interpolation method.

21 pages