Dirichlet quotients and 2D period Navier-Stokes equations

Peter Constantin; Ciprian Foias; Igor Kukavica; Andrew J. Majda

doi:10.1016/S0021-7824(97)89948-5

Dirichlet quotients and 2D period Navier-Stokes equations

Peter Constantin, Ciprian Foias, Igor Kukavica, Andrew J. Majda

Research output: Contribution to journal › Article › peer-review

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
DOIs	https://doi.org/10.1016/S0021-7824(97)89948-5
State	Published - Feb 1997

Keywords

Dirichlet quotients
Euler equation
Navier-stokes equations

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1016/S0021-7824(97)89948-5

Cite this

@article{1e301a3efcf14722a90eba79c2dfd572,

title = "Dirichlet quotients and 2D period Navier-Stokes equations",

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.",

keywords = "Dirichlet quotients, Euler equation, Navier-stokes equations",

author = "Peter Constantin and Ciprian Foias and Igor Kukavica and Majda, {Andrew J.}",

note = "Funding Information: The work of P. Constantin was supported by NSF DMS-9207080 and DOE DE FG02-92ER-25 119, that of C. Foias and I. Kukavica by NSF DMS-9024769, NSF DMS-9623 161, DOE DE-FG02-92ER25 120, and NAVY NOOO14-91 -J-l 140, while that of A. J. Majda by NSF DMS-99301094, ARPA NOOO14-92-J-1796, ONR NOOOl4-89-J-1044.P00003, and AR0 DAAL03-92-G-0010.",

year = "1997",

month = feb,

doi = "10.1016/S0021-7824(97)89948-5",

language = "English (US)",

volume = "76",

pages = "125--153",

journal = "Journal des Mathematiques Pures et Appliquees",

issn = "0021-7824",

publisher = "Elsevier Masson s.r.l.",

number = "2",

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TY - JOUR

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

AU - Constantin, Peter

AU - Foias, Ciprian

AU - Kukavica, Igor

AU - Majda, Andrew J.

N1 - Funding Information: The work of P. Constantin was supported by NSF DMS-9207080 and DOE DE FG02-92ER-25 119, that of C. Foias and I. Kukavica by NSF DMS-9024769, NSF DMS-9623 161, DOE DE-FG02-92ER25 120, and NAVY NOOO14-91 -J-l 140, while that of A. J. Majda by NSF DMS-99301094, ARPA NOOO14-92-J-1796, ONR NOOOl4-89-J-1044.P00003, and AR0 DAAL03-92-G-0010.

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

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U2 - 10.1016/S0021-7824(97)89948-5

DO - 10.1016/S0021-7824(97)89948-5

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SN - 0021-7824

VL - 76

SP - 125

EP - 153

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

IS - 2

ER -

Dirichlet quotients and 2D period Navier-Stokes equations

Abstract

Keywords

ASJC Scopus subject areas

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