The Navier-Stokes problem in a two-dimensional domain with angular outlets to infinity. (English. Russian original) Zbl 0979.35115

Nazarov, S. A.

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).

Reviewer: Oleg Dementiev (Chelyabinsk)

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

Keywords:

Navier-Stokes problem; angular outlets to infinity; two-dimensional domain