Global well-posedness for the MHD-Boussinesq system with the temperature-dependent viscosity

In this paper, we study the Cauchy problem for the MHD-Boussinesq system with the temperature-dependent viscosity. We first establish the local well-posedness for this system in Rd(d=2,3) by fully using the advantage of weighted function generated by heat kernel and Fourier localization technique. As a byproduct, we present a Beale-Kato-Majda type blow-up criterion. Then, under the assumptions on the viscosity coefficient is sufficiently close to some positive constant in L∞ norm, we can also get a global solution for this system in R2.