  We show that the Euler system of gas dynamics in $\mathbb{R}^d$, $d=2,3$,
with positive far field density and arbitrary far field entropy, admits
infinitely many steady solutions with compactly supported velocity. The same
proof yields a similar result for the incompressible Euler system with variable
density. In particular, these are examples of global in time smooth
(non-trivial) solutions for the corresponding time-dependent systems.
