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Russian Mathematical Surveys, 2005, Volume 60, Issue 5, Pages 849–873
DOI: https://doi.org/10.1070/RM2005v060n05ABEH003735 (Mi rm1642) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Diagrammatic approach to the 3D Navier–Stokes system

Ya. G. Sinaiab

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Princeton University, Department of Mathematics
English version PDF (292 kB) Citations (15)
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DOI: https://doi.org/10.1070/RM2005v060n05ABEH003735
Abstract: This paper concerns the 3-dimensional Navier–Stokes system (NSS) on $\mathbb R^3$ which describes the dynamics of viscous incompressible fluids without external forcing. For bounded initial conditions with compact support a locally convergent series is constructed which gives the solution of the NSS and whose coefficients are multidimensional integrals called diagrams. Estimates are given for various classes of diagrams and it is shown in particular that simple diagrams decay faster than exponentially.
Received: 18.08.2005
Russian version:
Uspekhi Matematicheskikh Nauk, 2005, Volume 60, Issue 5(365), Pages 47–70
DOI: https://doi.org/10.4213/rm1642
Bibliographic databases:
Document Type: Article
UDC: 517.957
MSC: Primary 35Q30; Secondary 35C10, 76D07
Language: English
Original paper language: Russian
Citation: Ya. G. Sinai, “Diagrammatic approach to the 3D Navier–Stokes system”, Uspekhi Mat. Nauk, 60:5(365) (2005), 47–70; Russian Math. Surveys, 60:5 (2005), 849–873
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:110
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