= Force flux at infinity in Stokes flow
{title2=$\mathbf F=\int_{S_R}\boldsymbol\sigma\mathbf n\,dS$}
In a three-dimensional exterior <Stokes flow> with no <body force>, $\nabla\cdot\boldsymbol\sigma=0$. The <divergence theorem> on the fluid between a rigid body and a large sphere $S_R$ gives the displayed force on the body, where $\mathbf n$ points outward from the sphere. The body's outward normal points oppositely to the inner normal of this fluid domain. A nonzero resultant <force> produces a leading <Stokeslet>, so <velocity> is $O(R^{-1})$, gauge-fixed <pressure> is $O(R^{-2})$ and <rate-of-strain tensor> is $O(R^{-2})$. The finite force is therefore compatible with pointwise decay of the <stress tensor>. Force-free bodies may have faster decay.
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