Greens Identities for the Momentum Equations

In order to obtain Green s identities for the flow field (u,p), a vector z is defined as the dot product of the stress tensor a(u, p) and a second solenoidal vector field v (divergence-free). The divergence or Gauss Theorem (10.1.1) is applied to the vector z 

The chain rule for differentiating the volume integral of eqn. (10.69) and the following identities [50] 

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