Quarter of a Sphere S given by the equation :
$ x^{2}+y^{2}+z^{2} = 16 \; \; $ with $, \; \; y\geq 0 \; \; ,\; \; z\geq 0$ oriented to the point $(0,2\sqrt{2},2\sqrt{2})$ with a normal vector $\vec{n}=\frac{\sqrt{2}}{2}\vec{j}+\frac{\sqrt{2}}{2}\vec{k}$
How can we calculate the flow of the vector field :
$\vec{F}(x,y,z)=\sin(y^{2}z^{2})\vec{i}+(2-xy)\vec{j}+z^{2}\vec{k}$