# Papkovich–Neuber solution

It can be shown that any Stokes flow with body force ${\displaystyle \mathbf {f} =0}$ can be written in the form:
${\displaystyle \mathbf {u} ={1 \over {2\mu }}\left[\nabla (\mathbf {x} \cdot \mathbf {\Phi } +\chi )-2\mathbf {\Phi } \right]}$
${\displaystyle p=\nabla \cdot \mathbf {\Phi } }$
where ${\displaystyle \mathbf {\Phi } }$ is a harmonic vector potential and ${\displaystyle \chi }$ 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.