On the inviscid limit of the viscous Boussinesq system with variable temperature diffusion

We prove the global-in-time well-posedness of the two-dimensional viscous Boussinesq system with temperature-dependent diffusivity under Yudovich-type initial data. Furthermore, we show that, as μ→0, the viscous solutions (vμ,θμ) converge to the inviscid solutions (v,θ) in L∞tLp for p∈[2,∞[, with an explicit rate of convergence.