  We consider entire solutions $u$ of the equations describing the stationary
flow of a generalized Newtonian fluid in 2D concentrating on the question, if a
Liouville-type result holds in the sense that the boundedness of $u$ implies
its constancy. A positive answer is true for $p$-fluids in the case $p>1$
(including the classical Navier-Stokes system for the choice $p=2$), and
recently we established this Liouville property for the Prandtl-Eyring fluid
model, for which the dissipative potential has nearly linear growth. Here we
finally discuss the case of perfectly plastic fluids whose flow is governed by
a von Mises-type stress-strain relation formally corresponding to the case
$p=1$. it turns out that, for dissipative potentials of linear growth, the
condition of $\mu$-ellipticity with exponent $\mu<2$ is sufficient for proving
the Liouville theorem.
