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Papkovich-Neuber solution

The Papkovich-Neuber solution is a technique for solving the Newtonian incompressible Stokes equations analytically. It can be shown that any Stokes flow with body force \mathbf{f}=0 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.

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Papkovich-Neuber_solution". A list of authors is available in Wikipedia.
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