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The Navier-Stokes problem in a two-dimensional domain with angular outlets to infinity. (English. Russian original) Zbl 0979.35115
J. Math. Sci., New York 108, No. 5, 790-805 (2002); translation from Zap. Nauchn. Semin. POMI. 257, 207-227 (1999).
The Navier-Stokes problem in a plane domain with two angular outlets to infinity, as usual, is supplied either by the flux condition or by the pressure drop one. It is proven for small data that there exists a solution with the velocity field decay \(O(|x|^{-1})\) as \(|x|\to \infty\) (if one of the angles is equal or greater than \(\pi\), additional symmetry assumptions are needed). Since the nonlinear terms are asymptotically of the same power, the results are based on the complete investigation of the linearized Stokes problem in weighted spaces with detached asymptotics (angular parts in the representations are not fixed).

MSC:
35Q30 Navier-Stokes equations
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
35B40 Asymptotic behavior of solutions to PDEs
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