Solution
= Solution
Axisymmetry and <incompressible flow>[incompressibility] give
$$
0=\nabla\cdot\mathbf u
=\frac1r\frac{d}{dr}(ru_r).
$$
Thus $ru_r=C$. Finiteness at the origin forces $C=0$, so
$$
\boxed{u_r=0}.
$$
= Solution
Axisymmetry and <incompressible flow>[incompressibility] give
$$
0=\nabla\cdot\mathbf u
=\frac1r\frac{d}{dr}(ru_r).
$$
Thus $ru_r=C$. Finiteness at the origin forces $C=0$, so
$$
\boxed{u_r=0}.
$$