Title: Initial-boundary value problem to 2D Boussinesq equations for MHD convection with stratification effects,
Abstract: This paper is concerned with the initial-boundary value problem to 2D
magnetohydrodynamics-Boussinesq system with the temperature-dependent
viscosity, thermal diffusivity and electrical conductivity. First, we establish
the global weak solutions under the minimal initial assumption. Then by
imposing higher regularity assumption on the initial data, we obtain the global
strong solution with uniqueness. Moreover, the exponential decay estimate of
the solution is obtained.