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Lorentz reciprocal theorem for Stokes flow

For two Stokes velocity-stress fields in the same domain,

\int_{\partial D} u^{(1)} \cdot σ^{(2)} n d S = \int_{\partial D} u^{(2)} \cdot σ^{(1)} n d S .

It follows by integrating the divergence of the corresponding cross-work flux and using symmetry of the Newtonian stress.

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