# irrotational field

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

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

Title irrotational field IrrotationalField 2013-03-22 13:09:05 2013-03-22 13:09:05 mathcam (2727) mathcam (2727) 9 mathcam (2727) Definition msc 26B12 irrotational vector field curl free field curl-free vector field Curl LaminarField