Frequency decay for Navier–Stokes stationary solutions

Abstract We consider stationary Navier–Stokes equations in R 3 with a regular external force and we prove the exponential frequency decay of the solutions. Moreover, if the external force is small enough, we give a pointwise exponential frequency decay for such solutions. If a damping term is added to the equation, a pointwise decay is obtained without the smallness condition over the force.