  In this paper we study the uniqueness property of solutions to the steady
incompressible Euler equations with perturbations in $\Bbb R^N$. Our
perturbations include as special cases the Euler equations with a `single
signed' nonlinear term, the self-similar Euler equations, and the steady
Navier-Stokes equations. For these equations show that suitable decay
assumptions at infinity on the solution or its derivatives, imposed by the
$L^q$ conditions imply that the only possible solution is zero.
