Abstract
Abstract In this Note we show that the asymptotic behaviour of a smooth function with bounded Dirichlet integral in an exterior domain is controlled by the asymptotic behaviour of its first Fourier coefficient. If the function is a velocity solution to the exterior Dirichlet problem for the steady two-dimensional Navier–Stokes equations we can strengthen this result, by proving the pointwise asymptotic convergence of the velocity solution to its asymptotic mean value, i.e., to the asymptotic finite limit of its first Fourier coefficient.
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