  The large time behavior of the unique strong solution to the barotropic
compressible Navier-Stokes system is studied with large external forces and
initial data, where the shear viscosity is a positive constant and the bulk one
is proportional to a power of the density. Some uniform estimates on the
Lp-norm of the density are established, and then deduce that the density
converges to its steady state in Lp-spaces, which transforms the large external
force into a small one in some sense. Moreover, to deal with the obstacles
brought by boundary, the conformal mapping and the pull back Green function are
applied to give a point-wise representation of the effective viscous flux, and
then make use of slip boundary conditions to cancel out the singularity.

Analysis of PDEs