On the global well‐posedness and striated regularity of the 2D Boussinesq‐MHD system.

In this paper, we investigate the global existence and uniqueness of strong solutions to the two‐dimensional Boussinesq‐MHD equations without the temperature diffusion for general initial data in Hm$$ {H}^m $$ with m>2$$ m>2 $$. As an application, we shall prove the propagation of the Hm+1$$ {H}^{m+1} $$ regularity of the interface between fluids with different temperatures. [ABSTRACT FROM AUTHOR]