Global well-posedness and analyticity for the 3D fractional magnetohydrodynamics equations in variable Fourier–Besov spaces

In this paper, we obtain the global well-posedness and analyticity of the 3D fractional magnetohydrodynamics equations in the critical variable Fourier–Besov spaces, which can be seen as a meaningful complement to the corresponding results of the magnetohydrodynamics equations in usual Fourier–Besov spaces. Moreover, our results are also new for the MHD equations (i.e., in the case of the classical dissipation $\alpha =1$).