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Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 7
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Articles

Convergence rate of stationary solutions to outflow problem for full Navier–Stokes equations

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Pages 1267-1288 | Received 06 Nov 2017, Accepted 15 Dec 2017, Published online: 29 Dec 2017
 

ABSTRACT

This paper is concerned with the large-time behavior of solutions to the outflow problem of full compressible Navier–Stokes equations for the general gas including ideal polytropic gas in the half line R+=(0,), where the gas flows out through the boundary. We first give some necessary and sufficient conditions for the existence of the stationary solution with the aid of center manifold theory. We also show the time asymptotic stability of the nondegenerate stationary solution under smallness assumptions on the boundary data and the initial perturbation in the Sobolev space, by employing an energy method. Moreover, the exponential and algebraic decay of the solution toward the supersonic stationary solution is obtained, provided that the initial perturbation belongs to the Sobolev space with exponential and algebraic weight respectively.

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Acknowledgements

The authors would like to thank the referees for their valuable comments.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was partially supported by National Natural Sciences Foundation of China [grant number 11671027], [grant number 11471321], [grant number 11371348].

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