Geodesic
Diagrammatic approach to the 3D Navier--Stokes system
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 60 (2005) no. 5, pp. 849-873

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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. 
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     author = {Ya. G. Sinai},
     title = {Diagrammatic approach to the {3D} {Navier--Stokes} system},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {849--873},
     publisher = {mathdoc},
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     number = {5},
     year = {2005},
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     url = {http://geodesic.mathdoc.fr/item/RM_2005_60_5_a1/}
}
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Ya. G. Sinai. Diagrammatic approach to the 3D Navier--Stokes system. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 60 (2005) no. 5, pp. 849-873. http://geodesic.mathdoc.fr/item/RM_2005_60_5_a1/