= Flow-free rotation of a spherical squirmer
A spherical <squirmer> can rotate without disturbing the surrounding fluid if its prescribed surface slip exactly cancels the velocity of rigid rotation: $u'=-\Omega\times an$. The laboratory-frame boundary velocity is then zero. <Uniqueness of Stokes flow> with decay at infinity gives identically zero exterior velocity. In particular $u'=b_0\sin\theta\,e_\phi$ gives $\Omega=-(b_0/a)e_z$. The cancellation concerns the total fluid boundary velocity, not the solid material's angular velocity.
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