Corner expansion of pressure-driven sector flow (source code)

= Corner expansion of pressure-driven sector flow
{title2=$\lambda_n=(2n+1)\pi/(2\alpha)$}

In a symmetric wedge $|\theta|<\alpha$, a constant Poisson forcing admits the particular solution $r^2(\cos2\theta/\cos2\alpha-1)/4$, 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 $\Delta(r^2\log r\cos2\theta)=4\cos2\theta$.