# irrotational field

Suppose $\mathrm{\Omega}$ 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 |