  In this paper, we study the nonlinear asymptotic stability of the Couette
flow in the stably stratified regime, namely the Richardson number
$\gamma^2>\frac{1}{4}$. Precisely, we prove that if the initial perturbation
$(u_{in},\vartheta_{in})$ of the Couette flow $v_s=(y,0)$ and the linear
temperature $\rho_s=-\gamma^2y+1$ satisfies
$\|u_{in}\|_{H^{s+1}}+\|\vartheta_{in}\|_{H^{s+2}}\leq
\epsilon_0\nu^{\frac{1}{2}}$, then the asymptotic stability holds.
