  In this paper, we study the Bresse system in a bounded domain with linear
frictional dissipation working only on the veridical displacement. The
longitudinal and shear angle displacements are free. Our first main result is
to prove that, independently from the velocities of waves propagations, this
linear frictional dissipation does not stabilize exponentially the whole Bresse
system. Our second main result is to show that the solution converges to zero
at least polynomially. The proof of the well-posedness of our system is based
on the semigroup theory. The stability results will be proved using a
combination of the energy method and the frequency domain approach.
