Global well-posedness of 2D nonlinear Boussinesq equations with mixed partial viscosity and thermal diffusivity

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.