Global existence and large-time behavior of solutions to one-dimensional compressible Navier–Stokes system with outer pressure in the half-space

The outer pressure problem of the compressible Navier–Stokes system in the Lagrangian coordinate system describing the one-dimensional motion of a viscous heat-conducting prefect polytropic gas in half-space is studied. Both the specific volume and the temperature are proved to be bounded from below and above independently of both space and time, and as a direct consequence, the global existence and large-time behavior of strong solutions for the outer pressure problem in the half-space is also obtained.