= Solution
For an incompressible Newtonian fluid at low <Reynolds number>, the quasi-steady <Stokes equations> are
$$
\boxed{\nabla\cdot\mathbf u=0,\qquad
-\nabla p+\mu\nabla^2\mathbf u+\rho\mathbf g=0,\qquad \mu=\rho\nu.}
$$
The first equation expresses local conservation of volume for constant density; the second balances <pressure>, viscous stresses and body force with negligible inertia. Convective inertia is negligible when $\mathrm{Re}=U\ell/\nu\ll1$ at the relevant flow scale. Quasi-steady flow also requires the viscous diffusion time $\ell^2/\nu$ to be short compared with the evolution time. Low convective <Reynolds number> alone does not justify neglecting a rapidly oscillating unsteady acceleration.
For a thin layer, slenderness further changes the comparison of longitudinal and transverse derivatives; these scalings, as well as low inertia, are needed for <lubrication theory>.
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