# solenoidal field

A solenoidal vector field is one that satisfies

$$\beta \x88\x87\beta \x8b\x85\mathrm{\pi \x9d\x90\x81}=0$$ |

at every point where the vector field $\mathrm{\pi \x9d\x90\x81}$ is defined. Here $\beta \x88\x87\beta \x8b\x85\mathrm{\pi \x9d\x90\x81}$ is the divergence.

This condition actually implies that there exists a vector $\mathrm{\pi \x9d\x90\x80}$, such that

$$\mathrm{\pi \x9d\x90\x81}=\beta \x88\x87\Gamma \x97\mathrm{\pi \x9d\x90\x80}.$$ |

For a function $f$ satisfying Laplaceβs equation

$${\beta \x88\x87}^{2}\beta \x81\u2018f=0,$$ |

it follows that $\beta \x88\x87\beta \x81\u2018f$ is solenoidal.

Title | solenoidal field |
---|---|

Canonical name | SolenoidalField |

Date of creation | 2013-03-22 13:09:02 |

Last modified on | 2013-03-22 13:09:02 |

Owner | giri (919) |

Last modified by | giri (919) |

Numerical id | 9 |

Author | giri (919) |

Entry type | Definition |

Classification | msc 26B12 |

Synonym | solenoidal |

Related topic | SourcesAndSinksOfVectorField |