Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 321 / 2 / a / Solution

The azimuthal momentum equation with $u_y=-3\Omega x/2$ isHence the slow radial drift isSubstitution into mass conservation, ${\partial }_t\Sigma +{\partial }_x(\Sigma u_x)=0$, gives the nonlinear diffusion equationIt describes slow axisymmetric viscous spreading while the velocity remains close to the imposed Kepler shear. It omits epicyclic and acoustic waves, rapid transients, self-gravity, nonaxisymmetric structure, and edge dynamics for which the assumed shear and secular force balance fail.