### Abstract

A simple qualitative one‐dimensional model for the 3‐D vorticity equation of incompressible fluid flow is developed. This simple model is solved exactly; despite its simplicity, this equation retains several of the most important structural features in the vorticity equations and its solutions exhibit some of the phenomena observed in numerical computations for breakdown for the 3‐D Euler equations.

Original language | English (US) |
---|---|

Pages (from-to) | 715-724 |

Number of pages | 10 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 38 |

Issue number | 6 |

DOIs | |

State | Published - 1985 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*38*(6), 715-724. https://doi.org/10.1002/cpa.3160380605

**A simple one‐dimensional model for the three‐dimensional vorticity equation.** / Constantin, P.; Lax, P. D.; Majda, A.

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 38, no. 6, pp. 715-724. https://doi.org/10.1002/cpa.3160380605

}

TY - JOUR

T1 - A simple one‐dimensional model for the three‐dimensional vorticity equation

AU - Constantin, P.

AU - Lax, P. D.

AU - Majda, A.

PY - 1985

Y1 - 1985

N2 - A simple qualitative one‐dimensional model for the 3‐D vorticity equation of incompressible fluid flow is developed. This simple model is solved exactly; despite its simplicity, this equation retains several of the most important structural features in the vorticity equations and its solutions exhibit some of the phenomena observed in numerical computations for breakdown for the 3‐D Euler equations.

AB - A simple qualitative one‐dimensional model for the 3‐D vorticity equation of incompressible fluid flow is developed. This simple model is solved exactly; despite its simplicity, this equation retains several of the most important structural features in the vorticity equations and its solutions exhibit some of the phenomena observed in numerical computations for breakdown for the 3‐D Euler equations.

UR - http://www.scopus.com/inward/record.url?scp=84990556249&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990556249&partnerID=8YFLogxK

U2 - 10.1002/cpa.3160380605

DO - 10.1002/cpa.3160380605

M3 - Article

VL - 38

SP - 715

EP - 724

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 6

ER -