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
Canonical name	IrrotationalField
Date of creation	2013-03-22 13:09:05
Last modified on	2013-03-22 13:09:05
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	9
Author	mathcam (2727)
Entry type	Definition
Classification	msc 26B12
Synonym	irrotational vector field
Synonym	curl free field
Synonym	curl-free vector field
Related topic	Curl
Related topic	LaminarField