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Decay Estimates for Steady Solutions of the Navier--Stokes Equations in Two Dimensions in the Presence of a Wall
2012
SIAM Journal on Mathematical Analysis
Let ω be the vorticity of a stationary solution of the two-dimensional Navier-Stokes equations with a drift term parallel to the boundary in the half-plane Ω + = {(x, y) ∈ R 2 | y > 1}, with zero Dirichlet boundary conditions at y = 1 and at infinity, and with a small force term of compact support. Then |xyω(x, y)| is uniformly bounded in Ω + . The proof is given in a specially adapted functional framework, and the result is a key ingredient for obtaining information on the asymptotic behavior
doi:10.1137/110852565
fatcat:mitfp4itzbfozcoqrexmdnjrti