Can you just produce a vector field that has the given curl?
- Hollywood
Is there an alternative way of showing that a vector field G(x, y, z) with a given curl on R^{3} can exist except by showing that div(curl G)=0?
E.g. Show that vector field G(x,y,z) exists, curl G=<xyz,-y^2z,yz^2>, without using the "div(curl G) = 0" relationship.