Suppose $\Omega$ is an open set in $\sR^3$ , and $\bV$ is a vector field with differentiable real (or possibly complex) valued component functions. If $\nabla\times \bV=0$ , then $\bV$ is called an irrotional vector field, or curl free field.

If $\bU$ and $\bV$ are irrotational, then $\bU\times\bV$ is solenoidal.