On the two-dimensional aperture problem for Navier-Stokes equations. (English. Abridged French version) Zbl 0860.35096

Nazarov, Serguei A.

C. R. Acad. Sci., Paris, Sér. I 323, No. 6, 699-703 (1996).

Summary: Existence of a solution to a two-dimensional aperture problem for the Navier-Stokes equations in weighted spaces with detached asymptotics at infinity is proved under symmetry and smallness assumptions on the problem data. This solution possesses a finite Dirichlet integral while the velocity field has the decay \(O(|x |^{-1})\) as \(|x|\to\infty\).

MSC:

35Q30	Navier-Stokes equations
35B40	Asymptotic behavior of solutions to PDEs
76D05	Navier-Stokes equations for incompressible viscous fluids

Keywords:

existence; aperture problem; Navier-Stokes equations; asymptotics at infinity; symmetry and smallness assumptions