= Forced annular displacement equation
{title2=$\sigma A_{xxx}-\beta\alpha_1A_t-\alpha_2AA_x=\beta\gamma_0F_t+\gamma_0^2FF_x+(\gamma_0^2/R)(AF)_x$}
A distinguished annular indentation limit has $\lambda^{-2}=O(\epsilon)$, $\lambda St=O(\epsilon)$ and $Re\gg\lambda\epsilon^{-3}$. Define $\beta=\lambda St/\epsilon$, $\sigma=(\lambda^2\epsilon)^{-1}\int_0^1u_0^2/(R+y)\,dy$, $\alpha_1=\gamma_0/R+\gamma_1/(R+1)$ and $\alpha_2=\gamma_0^2/R^2-\gamma_1^2/(R+1)^2$. Radial inertia supplies the pressure difference $\sigma A_{xx}$ between the walls. The axial momentum limits and the moving-wall condition supply its derivative, giving the displayed forced <KdV equation>. This reduction assumes the <viscous boundary layers> remain thin and their displaced flux is smaller than $O(\epsilon^2)$.
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