On the inviscid limit of the viscous Boussinesq system with variable temperature diffusion
Volume 137 / 2026
Annales Polonici Mathematici 137 (2026), 131-153
MSC: Primary 35Q35; Secondary 76D03, 76D05, 35B25, 35B45
DOI: 10.4064/ap250922-13-5
Published online: 28 October 2026
Abstract
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 $\mu \to 0$, the viscous solutions $(v_{\mu }, \theta _{\mu })$ converge to the inviscid solutions $(v, \theta )$ in $L^{\infty }_{t}L^{p}$ for $p\in [2, \infty \mathclose{[}$, with an explicit rate of convergence.
