Global properties of solutions to 1D-viscous compressiblebarotropic fluid equations with density dependent viscosity

The Navier-Stokes equations for compressible barotropic fluid in 1D with the massforce under zero velocity boundary conditions are studied. We prove the uniform upper andlower bounds for the density as well as the uniform in time L ²()-estimates for _x andu _x (u is the velocity). Moreover, a collection of the decay rate estimates for - (with being the stationary density) and u in ²()-norm and H ¹()-norm as time t areestablished. The results are given for general state function p() (but mainly monotone) andviscosity coefficient µ() of arbitrarily fast (or slow) growth as well as for the large data.