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# 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.

Related:

Curl, LaminarField

Synonym:

irrotational vector field, curl free field, curl-free vector field

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

26B12*no label found*

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