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The flux problem for the Navier-Stokes equations. (English. Russian original) Zbl 1319.35161
Russ. Math. Surv. 69, No. 6, 1065-1122 (2014); translation from Usp. Mat. Nauk 69, No. 6, 115-176 (2014).
This survey paper covers solution of the famous Leray problem [J. Leray, J. Math. Pures Appl. (9) 12, 1–82 (1933; Zbl 0006.16702); JFM 59.0402.01)] for incompressible Navier-Stokes equation in a multiconnected bounded domain (either in the 2D planar situation or in an axially symmetric domain) with inhomogeneous boundary conditions.
After an extensive review of the subject, they state the more recent existence results in the two aforementioned situations.

35Q30 Navier-Stokes equations
35Q31 Euler equations
76D05 Navier-Stokes equations for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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