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Some Uniform Estimates and Large-Time Behavior of Solutions to One-Dimensional Compressible Navier–Stokes System in Unbounded Domains with Large Data

Abstract

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.

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Correspondence to Jing Li.

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This work was partially supported by the National Center for Mathematics and Interdisciplinary Sciences, CAS, and NNSFC 11371348, 11525106, 11226163, and 11301422.

Communicated by T.-P. Liu

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Li, J., Liang, Z. Some Uniform Estimates and Large-Time Behavior of Solutions to One-Dimensional Compressible Navier–Stokes System in Unbounded Domains with Large Data. Arch Rational Mech Anal 220, 1195–1208 (2016). https://doi.org/10.1007/s00205-015-0952-0

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Keywords

  • Global Solution
  • Unbounded Domain
  • Stokes System
  • Large Initial Data
  • Global Generalize Solution