On the dimension of the attractors in two-dimensional turbulence

Peter Constantin; C. Foias; R. Temam

doi:10.1016/0167-2789(88)90022-X

On the dimension of the attractors in two-dimensional turbulence

Peter Constantin
, C. Foias
, R. Temam

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

179 Scopus citations

Abstract

Using a new version of the Sobolev-Lieb-Thirring inequality, we derive an upper bound for the dimension of the universal attractor for two-dimensional space periodic Navier-Stokes equations. This estimate is optimal up to a logarithmic correction. The relevance of this estimate to turbulence and related results are also briefly discussed.

Original language	English (US)
Pages (from-to)	284-296
Number of pages	13
Journal	Physica D: Nonlinear Phenomena
Volume	30
Issue number	3
DOIs	https://doi.org/10.1016/0167-2789(88)90022-X
State	Published - Apr 1988

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/0167-2789(88)90022-X

Cite this

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title = "On the dimension of the attractors in two-dimensional turbulence",

abstract = "Using a new version of the Sobolev-Lieb-Thirring inequality, we derive an upper bound for the dimension of the universal attractor for two-dimensional space periodic Navier-Stokes equations. This estimate is optimal up to a logarithmic correction. The relevance of this estimate to turbulence and related results are also briefly discussed.",

author = "Peter Constantin and C. Foias and R. Temam",

note = "Funding Information: This research was partially supported by the Applied Mathematical Sciences Program of the U.S. Department of Energy, Contract DE-AC02-82ER-12049 and Grant DE-FG02-86ER-25020; by the National Science Foundation, Grant DMS-860-2031; and the Research Fund of Indiana University. Also the first author is an A.P, Sloan Research Fellow.",

year = "1988",

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doi = "10.1016/0167-2789(88)90022-X",

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T1 - On the dimension of the attractors in two-dimensional turbulence

AU - Constantin, Peter

AU - Foias, C.

AU - Temam, R.

N1 - Funding Information: This research was partially supported by the Applied Mathematical Sciences Program of the U.S. Department of Energy, Contract DE-AC02-82ER-12049 and Grant DE-FG02-86ER-25020; by the National Science Foundation, Grant DMS-860-2031; and the Research Fund of Indiana University. Also the first author is an A.P, Sloan Research Fellow.

PY - 1988/4

Y1 - 1988/4

N2 - Using a new version of the Sobolev-Lieb-Thirring inequality, we derive an upper bound for the dimension of the universal attractor for two-dimensional space periodic Navier-Stokes equations. This estimate is optimal up to a logarithmic correction. The relevance of this estimate to turbulence and related results are also briefly discussed.

AB - Using a new version of the Sobolev-Lieb-Thirring inequality, we derive an upper bound for the dimension of the universal attractor for two-dimensional space periodic Navier-Stokes equations. This estimate is optimal up to a logarithmic correction. The relevance of this estimate to turbulence and related results are also briefly discussed.

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UR - https://www.scopus.com/pages/publications/0023999086#tab=citedBy

U2 - 10.1016/0167-2789(88)90022-X

DO - 10.1016/0167-2789(88)90022-X

M3 - Article

AN - SCOPUS:0023999086

SN - 0167-2789

VL - 30

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EP - 296

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 3

ER -

On the dimension of the attractors in two-dimensional turbulence

Abstract

All Science Journal Classification (ASJC) codes

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