# Difference between revisions of "Solution of the Blatter-Pattyn model"

\begin{align} & x:\quad 4\frac{\partial }{\partial x}\left( \eta \frac{\partial u}{\partial x} \right)+\frac{\partial }{\partial y}\left( \eta \frac{\partial u}{\partial y} \right)+\frac{\partial }{\partial z}\left( \eta \frac{\partial u}{\partial z} \right)=-2\frac{\partial }{\partial x}\left( \eta \frac{\partial v}{\partial y} \right)-\frac{\partial }{\partial y}\left( \eta \frac{\partial v}{\partial x} \right)+\rho g\frac{\partial s}{\partial x} \\ & y:\quad 4\frac{\partial }{\partial y}\left( \eta \frac{\partial v}{\partial y} \right)+\frac{\partial }{\partial x}\left( \eta \frac{\partial v}{\partial x} \right)+\frac{\partial }{\partial z}\left( \eta \frac{\partial v}{\partial z} \right)=-2\frac{\partial }{\partial y}\left( \eta \frac{\partial u}{\partial x} \right)-\frac{\partial }{\partial x}\left( \eta \frac{\partial u}{\partial y} \right)+\rho g\frac{\partial s}{\partial y} \\ \end{align}