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We consider the 3D steady Navier-Stokes system on the exterior of an infinitecylinder under the action of an external force. We are concerned with the classof solutions in which the velocity field is vertically uniform and at rest athorizontal infinity. This configuration includes the 2D exterior problem forthe steady Navier-Stokes system known to have characteristic difficulties. Weprove the existence of solutions in the above class for a given nonsymmetricexternal force with suitable decay. The proof can be adapted to the 2D problemand gives a generalization of H. (2023) in view of the regularity of solutions.

Existence of steady Navier-Stokes flows exterior to an infinite cylinder