  We study the equilibrium configurations of a possibly asymmetric
fluid-structure-interaction problem. The fluid is confined in a bounded planar
channel and is governed by the stationary Navier-Stokes equations with laminar
inflow and outflow. A body is immersed in the channel and is subject to both
the lift force from the fluid and to some external elastic force. Asymmetry,
which is motivated by natural models, and the possibly non-vanishing velocity
of the fluid on the boundary of the channel require the introduction of
suitable assumptions to prevent collisions of the body with the boundary. With
these assumptions at hand, we prove that for sufficiently small inflow/outflow
there exists a unique equilibrium configuration. Only if the inflow, the
outflow and the body are all symmetric, the configuration is also symmetric. A
model application is also discussed.
