Rotational Stokes flow between concentric spheres
= Rotational Stokes flow between concentric spheres
{c}
For concentric spheres of radii $a<b$, with the inner sphere rotating at angular velocity $\boldsymbol\Omega$ and the outer sphere fixed, the Stokes velocity is
$$
\mathbf u(\mathbf x)
=\frac{a^3}{b^3-a^3}
\left(\frac{b^3}{r^3}-1\right)
\boldsymbol\Omega\times\mathbf x.
$$
The pressure is constant, and may be set to zero.