Corner expansion of pressure-driven sector flow (${\lambda }_n=(2n+1)\pi /(2\alpha )$)

In a symmetric wedge $|\theta |<\alpha$, a constant Poisson forcing admits the particular solution $r^2(\cos 2\theta /\cos 2\alpha -1)/4$, except at resonant angles. Zero-wall harmonic corrections have exponents ${\lambda }_n=(2n+1)\pi /(2\alpha )$. If the smallest exponent is below two, the global boundary data make that homogeneous mode dominate the local quadratic forcing. If it is below one, the velocity gradient can be singular although the velocity vanishes. When an exponent equals two, the appropriate radial solution contains $r^2\log r$, since $\Delta (r^2\log r\cos 2\theta )=4\cos 2\theta$.