### Abstract

We consider the 2D Navier-Stokes equations on a square with periodic boundary conditions. Dividing the square into N equal subsquares, we show that if the asymptotic behavior of the average of solutions on these subsquares (finite volume elements) is known, then the large time behavior of the solution itself is completely determined, provided N is large enough. We also establish a rigorous upper bound for N needed to determine the solutions to the Navier-Stokes equation in terms of the physical parameters of the problem.

Original language | English (US) |
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Pages (from-to) | 165-174 |

Number of pages | 10 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 60 |

Issue number | 1-4 |

DOIs | |

State | Published - Nov 1 1992 |

Externally published | Yes |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics

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## Cite this

Jones, D. A., & Titi, E. S. (1992). Determining finite volume elements for the 2D Navier-Stokes equations.

*Physica D: Nonlinear Phenomena*,*60*(1-4), 165-174. https://doi.org/10.1016/0167-2789(92)90233-D