Solution
= Solution
For a unidirectional, $z$-independent velocity
$$
\mathbf u=u_z(r,\theta)\mathbf e_z,
$$
incompressibility holds automatically. The axial <Stokes flow> equation is
$$
0=-p_z+\mu\nabla_\perp^2u_z.
$$
No external pressure gradient is imposed, so $p_z=0$ and
$$
\boxed{\nabla_\perp^2u_z=0}.
$$
Thus the axial velocity is a <harmonic function> in the disk.