Some Uniform Estimates and Large-Time Behavior for One-Dimensional Compressible Navier-Stokes System in Unbounded Domains with Large Data

Understand

This paper is concerned with the large-time behavior of solutions to the initial and initial boundary value problems with large initial data for the compressible Navier-Stokes system describing the one-dimensional motion of a viscous heat-conducting perfect polytropic gas in unbounded domains.

• The temperature is proved to be bounded from below and above independently of both time and space.
• Moreover, the global solution is showed to be asymptotically stable as time tends to infinity.
• Note that the initial data can be arbitrarily large.