  We study solutions to the obstacle problem for the stationary Navier--Stokes
system in a~two dimensional exterior domain (flow past a prescribed body). We
prove that the classical Leray solution to this problem is always nontrivial.
No additional condition (on symmetry or smallness, etc.) is assumed. This is a
complete extension of a~classical result of C.J. Amick (Acta Math. 1988) where
nontriviality was proved under symmetry assumption.
