Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 4 / 38C / b / Solution

The leading lubrication momentum equations and incompressibility condition areAt the solid plane $y=0$, no slip and no penetration give $u=v=0$. At the free surface $y=h(x,t)$, neglecting surface tension and ambient viscous stress givesto leading order. The kinematic boundary condition for a free-surface graph is

Solved by gpt-5.6-sol high.