A new boundary problem for the two dimensional navier-stokes system

Efim Dinaburg; Dong Li; Yakov G. Sinai

doi:10.1007/s10955-009-9760-y

A new boundary problem for the two dimensional navier-stokes system

Efim Dinaburg
, Dong Li
, Yakov G. Sinai

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

3 Scopus citations

Abstract

We formulate a new boundary value problem for the 2D Navier-Stokes system on the unit square. Under some suitable assumptions on the initial velocity, we obtain quantitative decay estimates of the Fourier modes of both the vorticity and the velocity. It is found that in one direction the Fourier modes decay exponentially and along the other direction their decay is only power like.

Original language	English (US)
Pages (from-to)	737-750
Number of pages	14
Journal	Journal of Statistical Physics
Volume	135
Issue number	4
DOIs	https://doi.org/10.1007/s10955-009-9760-y
State	Published - May 2009

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Navier-Stokes equations

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10.1007/s10955-009-9760-y

Cite this

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title = "A new boundary problem for the two dimensional navier-stokes system",

abstract = "We formulate a new boundary value problem for the 2D Navier-Stokes system on the unit square. Under some suitable assumptions on the initial velocity, we obtain quantitative decay estimates of the Fourier modes of both the vorticity and the velocity. It is found that in one direction the Fourier modes decay exponentially and along the other direction their decay is only power like.",

keywords = "Navier-Stokes equations",

author = "Efim Dinaburg and Dong Li and Sinai, \{Yakov G.\}",

note = "Funding Information: Acknowledgements We thank C. Bardos, G. Seregin, E. Titi, V. Yakhot for numerous useful discussions. Special thanks go to N. Chernov for his collaboration, careful reading of the text and excellent numerical work which he did in connection with this paper. The first author acknowledges the support from the grant NCNIL 07-01-9221. The second author is supported in part by NSF DMS 0635607 and a start-up funding from Mathematics Department of University of Iowa. The third author acknowledges the financial support from NSF grant DMS 0600996.",

year = "2009",

month = may,

doi = "10.1007/s10955-009-9760-y",

language = "English (US)",

volume = "135",

pages = "737--750",

journal = "Journal of Statistical Physics",

issn = "0022-4715",

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T1 - A new boundary problem for the two dimensional navier-stokes system

AU - Dinaburg, Efim

AU - Li, Dong

AU - Sinai, Yakov G.

N1 - Funding Information: Acknowledgements We thank C. Bardos, G. Seregin, E. Titi, V. Yakhot for numerous useful discussions. Special thanks go to N. Chernov for his collaboration, careful reading of the text and excellent numerical work which he did in connection with this paper. The first author acknowledges the support from the grant NCNIL 07-01-9221. The second author is supported in part by NSF DMS 0635607 and a start-up funding from Mathematics Department of University of Iowa. The third author acknowledges the financial support from NSF grant DMS 0600996.

PY - 2009/5

Y1 - 2009/5

N2 - We formulate a new boundary value problem for the 2D Navier-Stokes system on the unit square. Under some suitable assumptions on the initial velocity, we obtain quantitative decay estimates of the Fourier modes of both the vorticity and the velocity. It is found that in one direction the Fourier modes decay exponentially and along the other direction their decay is only power like.

AB - We formulate a new boundary value problem for the 2D Navier-Stokes system on the unit square. Under some suitable assumptions on the initial velocity, we obtain quantitative decay estimates of the Fourier modes of both the vorticity and the velocity. It is found that in one direction the Fourier modes decay exponentially and along the other direction their decay is only power like.

KW - Navier-Stokes equations

UR - https://www.scopus.com/pages/publications/67650602101

UR - https://www.scopus.com/pages/publications/67650602101#tab=citedBy

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DO - 10.1007/s10955-009-9760-y

M3 - Article

AN - SCOPUS:67650602101

SN - 0022-4715

VL - 135

SP - 737

EP - 750

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 4

ER -

A new boundary problem for the two dimensional navier-stokes system

Abstract

All Science Journal Classification (ASJC) codes

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