 Viscous evolution of an accretion disk

Viscous evolution of an accretion disk follows the redistribution of surface density as internal stresses exchange angular momentum between rings. For an axisymmetric Keplerian disk without mass loss, combining mass and angular-momentum conservation gives ${\partial }_t\Sigma =(3/r){\partial }_r[r^{1/2}{\partial }_r(\nu \Sigma r^{1/2})]$. Here $\nu$ is an effective kinematic viscosity. The equation describes both inward accretion and outward spreading; the sign of local mass flow follows from the radial gradient, rather than viscosity alone.^[ref]