Stability threshold of the Poiseuille flow in 2D Navier-Stokes Boussinesq equations

We study the transition threshold problem for the 2D Navier--Stokes Boussinesq equations around the Poiseuille flow on three domains: $\mathbb{T} \times \mathbb{R}$, $\mathbb{T} \times [0, \infty)$, and $\mathbb{T} \times [-1, 1]$. More precisely, we prove that if the initial perturbations of the vo