Global well-posedness for the 212D Bénard system with partial viscosity terms

In this paper, we show the global well-posedness for the 212D Bénard equations with partial viscosity terms, i.e. (1) μ > 0 and κ=0; (2) μ=0 and κ > 0, which mean the zero thermal diffusivity and the zero viscous dissipation, respectively.