Incompressible Fluids With Const. Viskosities
from:
\frac{\delta \vec{v}}{\delta t} + \left( \vec{v} \cdot grad \right) \vec{v} = - \frac{1}{\rho} grad \ p + \nu \Delta \vec{v} + \vec{g}
follows:
div \ grad \ \Phi = 0
and thus in cartesian coordinates:
\frac{\delta \Phi^2}{\delta x^2} + \frac{\delta \Phi^2}{\delta y^2} = 0
and equally in x,y-coordinates:
\frac{\delta \Psi^2}{\delta x^2} + \frac{\delta \Psi^2}{\delta y^2} = 0