Can You Inverse a Curl Operator?

[calvinjhfeng]

It doesn't seem like I have seen such a thing. I want to know if there's an inverse Curl operator?

Let's say I was given the Curl of X = some function, now how can I solve for X ?
How do I inverse the curl on both side of the equation?

Thank you very much in advance.

 

[sunjin09]

take the curl again, assuming your original field is div-free, you end up with a vector poisson's equation