= Slowly opening Stokes wedge
{title2=$\psi=-\dot\alpha r^2G(\theta)/2$}
For a fixed wall at $\theta=0$ and a wall rotating at $\dot\alpha$ at $\theta=\alpha$, the <quasi-steady Stokes approximation> with the <no-slip boundary condition> gives
$$
G(\theta)=\frac{\sin\alpha(1-\cos2\theta)+\cos\alpha(\sin2\theta-2\theta)}{2(\sin\alpha-\alpha\cos\alpha)}.
$$
Indeed the <biharmonic equation> for $r^2G$ is $G^{(4)}+4G''=0$; the angular basis is $1,\theta,\sin2\theta,\cos2\theta$. The four wall conditions are $G(0)=G'(0)=G'(\alpha)=0$, $G(\alpha)=1$. The outward radial <volume flux per unit width> is $-r^2\dot\alpha/2$, precisely the negative rate of increase of wedge <area>. The associated local <pressure> is $p=\mu\dot\alpha[2\cos\alpha/(\sin\alpha-\alpha\cos\alpha)]\log(r/r_*)+C$. Its logarithmic singularity is integrable, although the ideal hinge requires a microscopic regularization.
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