### Abstract

We show that for the periodic 2D Navier-Stokes equations (NSE) the set of initial data for which the solution exists for all negative times and has exponential growth is rather rich. We study this set and show that it is dense in the phase space of the NSE. This yields to a positive answer to a question in [BT]. After an appropriate rescaling the large Reynolds limit dynamics on this set is Eulerian.

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

Pages (from-to) | 125-153 |

Number of pages | 29 |

Journal | Journal des Mathematiques Pures et Appliquees |

Volume | 76 |

Issue number | 2 |

State | Published - Feb 1997 |

### Fingerprint

### Keywords

- Dirichlet quotients
- Euler equation
- Navier-stokes equations

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Journal des Mathematiques Pures et Appliquees*,

*76*(2), 125-153.

**Dirichlet quotients and 2D period Navier-Stokes equations.** / Constantin, Peter; Foias, Ciprian; Kukavica, Igor; Majda, Andrew J.

Research output: Contribution to journal › Article

*Journal des Mathematiques Pures et Appliquees*, vol. 76, no. 2, pp. 125-153.

}

TY - JOUR

T1 - Dirichlet quotients and 2D period Navier-Stokes equations

AU - Constantin, Peter

AU - Foias, Ciprian

AU - Kukavica, Igor

AU - Majda, Andrew J.

PY - 1997/2

Y1 - 1997/2

N2 - We show that for the periodic 2D Navier-Stokes equations (NSE) the set of initial data for which the solution exists for all negative times and has exponential growth is rather rich. We study this set and show that it is dense in the phase space of the NSE. This yields to a positive answer to a question in [BT]. After an appropriate rescaling the large Reynolds limit dynamics on this set is Eulerian.

AB - We show that for the periodic 2D Navier-Stokes equations (NSE) the set of initial data for which the solution exists for all negative times and has exponential growth is rather rich. We study this set and show that it is dense in the phase space of the NSE. This yields to a positive answer to a question in [BT]. After an appropriate rescaling the large Reynolds limit dynamics on this set is Eulerian.

KW - Dirichlet quotients

KW - Euler equation

KW - Navier-stokes equations

UR - http://www.scopus.com/inward/record.url?scp=0031068506&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031068506&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031068506

VL - 76

SP - 125

EP - 153

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

SN - 0021-7824

IS - 2

ER -