  We study existence and stability of steady solutions of the isentropic
compressible Navier-Stokes equations on a finite interval with non
characteristic boundary conditions, for general not necessarily small-amplitude
data. We show that there exists a unique solution, about which the linearized
spatial operator possesses (i) a spectral gap between neutral and
growing/decaying modes, and (ii) an even number of nonstable eigenvalues ?
(with a nonnegative real part). In the case that there are no nonstable
eigenvalues, i.e., of spectral stability, we show this solution to be
nonlinearly exponentially stable in H2 X H3. Using "Goodman-type" weighted
energy estimates, we establish spectral stability for small-amplitude data. For
large amplitude data, we obtain high-frequency stability, reducing stability
investigations to a bounded frequency regime. On this remaining,
bounded-frequency regime, we carry out a numerical Evans function study, with
results again indicating universal stability of solutions.
