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Employing the approach of A. Takeshita [Pacific J. Math., Vol. 157 (1993),151--158], we give an elementary proof of the invalidity of the Leray-HopfExtension Condition for certain multiply connected bounded domains of R^n,n=2,3, whenever the flow through the different components of the boundary isnon-zero. Our proof is alternative to and, to an extent, more direct than therecent one proposed by J.G. Heywood [J. Math. Fluid Mech. Vol. 13 (2011),449--457].

On the Leray-Hopf Extension Condition for the Steady-State Navier-Stokes Problem in Multiply-Connected Bounded Domains