Given $\nabla \cdot u = 0$ and $w = \nabla \times u$ equation 9 of http://projecteuclid.org/euclid.cmp/1103941230 has the identity $u = - \nabla \times (\nabla^{-1} w)$.
What is $\nabla^{-1}$ exactly and how was this identity derived?
Thanks a lot.