# Math Help - Divergence reverse process

1. ## Divergence reverse process

can anyone plz tell me how to get F(vector field) when im given DIV F(div means divergence )

2. ## What makes you think it's possible?

$F=(-y,xy,z), divF=x+1$
$G=(x^2/2,y,-xy), divG=x+1$

3. well i think there will be some way ....

4. Well, you can always say: Let S be the set of all possible vector fields F such that div F=x+1. In that case, the two examples I just gave you would both be elements in S. But you seem to be asking your question with the assumption that there is a one-to-one correspondence between vector fields and their divergences. This is not the case.

5. To add further, since $\nabla \cdot \nabla \times {\bf F} = 0$ where ${\bf F}$ is an arbitrary vector field, then you can add $\nabla \times {\bf F}$ to your vector field and it will lead to the same diverence.