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JOURNALS // Uspekhi Matematicheskikh Nauk // Archive

Uspekhi Mat. Nauk, 2005 Volume 60, Issue 5(365), Pages 47–70 (Mi rm1642)

This article is cited 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

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.

UDC: 517.957

MSC: Primary 35Q30; Secondary 35C10, 76D07

Received: 18.08.2005

DOI: 10.4213/rm1642


 English version:
Russian Mathematical Surveys, 2005, 60:5, 849–873

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