Here, \Phi \in C^2(V, \mathbb{R}) is a scalar potential, \nabla \Phi is its gradient, and \nabla \cdot \mathbf{R} is the divergence of the vector field \mathbf{R}. The irrotational vector field \mathbf{G} is called a gradient field and \mathbf{R} is called a solenoidal field or rotation field. This decomposition does not exist for all vector fields and is not unique.
