Large-Time Behavior of Solutions to Compressible Navier-Stokes System in Unbounded Domains with Degenerate Heat-Conductivity and Large Data

TL;DR

This paper investigates the long-term behavior of solutions to the one-dimensional compressible Navier-Stokes equations with degenerate heat-conductivity in unbounded domains, establishing bounds and stability for large initial data.

Contribution

It proves uniform bounds and asymptotic stability of solutions with large initial data for a degenerate heat-conductivity model in unbounded domains.

Findings

Bounded specific volume and temperature independent of time and space.

Global solutions are asymptotically stable as time approaches infinity.

Results hold for large initial data in unbounded domains.

Abstract

We are 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 with degenerate heat-conductivity describing the one-dimensional motion of a viscous heat-conducting perfect polytropic gas in unbounded domains. Both the specific volume and temperature are proved to be bounded from below and above independently of both time and space. Moreover, it is shown that the global solution is asymptotically stable as time tends to infinity.