irrotational field

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

If $𝐔$ and $𝐕$ are irrotational, then $𝐔\times 𝐕$ is solenoidal.