Papkovich-Neuber solution

The Papkovich-Neuber solution is a technique for solving the Stokes flow with body force  can be written in the form:

$\mathbf{u} = {1\over{2 \mu}} \nabla ( \mathbf{x} \cdot \mathbf{\Phi} + \chi) - 2 \mathbf{\Phi}$

$p = \nabla \cdot \mathbf{\Phi}$

where $\mathbf{\Phi}$ is a harmonic vector potential and $χ$ is a harmonic scalar potential. The properties and ease of construction of harmonic functions makes the Papkovich-Neuber solution a powerful technique for solving the Stokes Equations in a variety of domains.