= Inviscid Couette initial-value Green function
{title2=$\widetilde v(y,t)=\int_{-1}^1G_k(y,s)e^{-i\alpha\lambda st}(D_s^2-k^2)\widetilde v_0(s)\,ds$}
For constant shear $U=\lambda y$, the wall-normal Laplacian of velocity is advected with phase $e^{-i\alpha\lambda yt}$. Inverting $D^2-k^2$, $k^2=\alpha^2+\beta^2$, with its <Dirichlet Green function> gives the displayed initial-value solution. Impermeable inviscid walls impose zero normal velocity, not zero tangential velocity or no-slip wall vorticity.
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