= Minimum-dissipation theorem for Stokes flow
{c}
Among all incompressible velocity fields with the same prescribed boundary velocity and far-field behavior, the <Stokes flow> minimizes <viscous dissipation>. If $\mathbf v=\mathbf u+\mathbf w$, where $\mathbf u$ is the Stokes solution and $\mathbf w$ has homogeneous boundary data, integration by parts and the Stokes equation eliminate the cross term, leaving
$$
\mathcal D[\mathbf v]-\mathcal D[\mathbf u]
=2\mu\int\mathbf e(\mathbf w):\mathbf e(\mathbf w)\,dV\geq0.
$$
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