  In this paper, we discuss with the global well-posedness of 2D anisotropic
nonlinear Boussinesq equations with any two positive viscosities and one
positive thermal diffusivity. More precisely, for three kinds of viscous
combinations, we obtain the global well-posedness without any assumption on the
solution. For other three difficult cases, under the minimal regularity
assumption, we also derive the unique global solution. To the authors'
knowledge, our result is new even for the simplified model.
