Some uniform estimates and large-time behavior of solutions to one-dimensional compressible Navier-Stokes system in unbounded domains with large data. (English) Zbl 1334.35242
Summary: We study 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, independent of both time and space. Moreover, it is shown that the global solution is asymptotically stable as time tends to infinity. Note that the initial data can be arbitrarily large. This result is proved by using elementary energy methods.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76N15 | Gas dynamics (general theory) |
| 35B40 | Asymptotic behavior of solutions to PDEs |
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