Viscous spreading of a narrow planetary ring
= Viscous spreading of a narrow planetary ring
In a local Keplerian sheet, slow viscous drift gives $\partial_t\Sigma=3\partial_x^2(\nu\Sigma)$. For $\nu=A\Sigma^2$, the compact profile $\Sigma=\sigma\sqrt{1-x^2/w^2}$ preserves its shape, conserves $\sigma w$, and spreads with $w\propto t^{1/4}$ at late times.