Integral Formulation for the Momentum Equations

Similar to scalar field problems, in order to obtain an integral representation for the momentum eqns. (10.63) and (10.64) for the flow field (u, p), Green s formulae for the momentum equations (Theorems (10.2.1) and (10.2.2)) are used together with the fundamental singular solution of Stokes equations, i.e., 

Here u (x - xo) represents the velocity field generated by a point force in the -direction at a point x0 and qk is the corresponding pressure. 

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