The generalized MHD-Boussinesq equations are studied in this paper. The well-posedness of the strong solutions for the generalized MHD-Boussinesq equations is proved. Asymptotic regularity for the generalized MHD-Boussinesq equations is proved in $H^{\frac{9}{2}}\times H^{\frac{9}{2}}\times H^{\frac{9}{2}}$. The higher regularity for the generalized MHD-Boussinesq equations is proved in $H^{a}\times H^{a}\times H^{a}$ for $a\geq\frac{9}{2}$.

The multi-dimensional hyperviscous magnetohydrodynamics equation is considered in this paper. The well-posedness of the multi-dimensional hyperviscous magnetohydrodynamics equation is proved. Global attractor of the multi-dimensional hyperviscous magnetohydrodynamics equations is proved in Η1/2+n/4×Η1/2+n/4 and Η1+n/2×Η1+n/2.